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Decomposition approaches to modelling LAN contention and host computer performance
Decomposition approaches to modelling LAN contention and host computer performance Andre B Bondi examines the effect of contention on token ring and CSMA networks
Networks consisting of special-purpose workstations connected by local area networks have become very popular. Their use may grow to the point where LAN contention degrades the performance of the application, e.g. in graphics workstations whose images must be updated frequently or in applications involving large file transfers. Methods of predicting the level of I_ANcontention and its effect on host performance are discussed, and the way in which this problem affects token rings and CSMAtype networks is examined. Keywords: computer networks, performance, LAN contention, token ring networks, CSMA networks, mathematical modelling
In recent years, it has become economically feasible to connect several workstations, mainframe, mini and personal computers via a local area network (LAN). Many minicomputers have speeds similar to those of mainframes, but because they are often running only a few jobs at a time, they are able to offer traffic to the LAN at rates that may be considerably higher than those offered by mainframes, which may be executing many jobs concurrently. In addition, minicomputers may support applications such as file transfers and high-speed image Department of Computer Science,University of California,SantaBarbara, CA 93106, USA
processing, which require the movement of large volumes of data and have stringent timing constraints. It is therefore likely that LAN utilization may exceed the low levels (less than 10%) reported in Reference I. Reasonable network access times may not be feasible at utilizations as low as 30% on some network media; on CSMA-type networks, for instance, access times escalate even at moderate loads because of repeated collisions. Of course, the load offered to a LAN depends on the rate at which hosts can generate packets for transmission. This depends not only on the processing requirements of higher level protocols, but also on the usage of the CPU and I/O devices at each host. Only the latter usage is considered here. If the CPU is heavily loaded by application work, packets may not be generated fast enough to cause severe network contention. On the other hand, if the CPU is moderately loaded and the application requires that repeated enquiries be made of a remote file server, the network loading may be substantial. This paper discusses techniques for predicting LAN loading in terms of the workloads at individual host computers. The techniques presented here may also be used to analyse such problems as file placement on workstations, file servers and conventional mainframes. Lazowska et al., 2 Sauer and Chandy3 and Ferrari4 have discussed the relevant performance-evaluation techniques. In systems in which packet generation corresponds to I/0, the process that generates a packet may be blocked until transmission has been completed. Consequently, network contention may have a detrimental effect on host performance. The problem of modelling such
0140-3664/87/020070-09 $03.00 © 1987 Butterworth & Co (Publishers) Ltd 70
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systems is similar to that of modellinga disc shared by two or more CPUs s' 6, because the load offered to the network by each host influences the performance of the other hosts. A shared disc with a single path may be modelled as a server which is accessed via a FCFSqueue common to all of the conneced CPUs. The problem is more complicated for LANs, because hosts do not usually access the network in an order susceptible to analytical modelling such as FCFS, processor sharing, or pure delay (infinite service). For instance, token rings such as the Zurich rings and ProNet 7' 8 and CSMA buses like Ethernet9 have very different access methods and consequently have different performance characteristics under light and heavy loads 1°. The token rings use the nonexhaustive service discipline, i.e. each host is allowed to transmit at most one packet during every complete cycle of the token. With Ethernet, all stations may attempt to transmit at any time. If two or more attempt transmission simultaneously, they must back off for random intervals and try to transmit again. These characteristics must be taken into account when formulating a performance model of the entire system N' 12. Rather than developing entirely new tools to address the problem, a system of hosts will be decomposed into separate units, each of which will be modelled using wellknown queueing network algorithms for obtaining performance measures such as those described in References 2 and 13-15. These algorithms may be combined with LAN models to produce a model of the complete system. Two modelling approaches will be examined. The first approach 11'12 is applicable to networks in which the media access mechanism selects hosts to transmit data in turn, such as the Zurich and ProNet rings7' 8. The second approach 2'16 is applicable to contention-based access mechanisms such as CSMA 9 and slotted rings such as the Cambridge ring 17. In both of these, the network access discipline is symmetrical in the sense that the medium can be acquired immediately if it is available. The second approach has been successfully used by Lazowska et al. to model a system consisting of single-user workstations connected to a file server via an Ethernet18. Both approaches will be analysed and the merits and deficiencies of each will be discussed. Some extensions will also be proposed. It should be emphasized that the extensions have not been validated against either live or simulated data. However, they are presented in order to give the reader a flavour of some possible approaches to model development.
MODELLING A TOKEN RING'S IMPACT ON HOST'S PERFORMANCE Method of apparent coefficients of variation ALAN may be regarded as a device that is accessed via a gateway attached to each of the host computers it connects. In the absence of buffering, a job will move to its host's gateway every time it generates a packet and then return to the CPU once transmission of the packet is
vol 10 no 2 april 1987
oil0\
HostO
ILl
CPUO
i I
~
I I I
Gate~ Disc1
H ~ o s t l CPU1
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Figure 1. Token ring connected to two hosts; represents the model used in the method of apparent coefficients of variation: Z ~ FCFS server, ®/_AN, discipline unspecified complete, as illustrated in Figure 1. In this respect, a gateway is no different from the secondary storage device in the central server model 13. However, the waiting time of a job at the gateway is influenced not only by the workload characteristics of the host, but also by the traffic at other hosts. It follows that the network access delay at one host depends on the workload characteristics of the other hosts and vice versa. A packet may spend time at the head of a gateway dispatch queue without actually receiving service. This time will be termed the packet blocking delay. The distribution of the packet blocking delay is not exponential in general. This violates one of the basic assumptions of closed queueing network models solvable by exact methods 19. However, a fast method for solving closed queueing network models with nonexponential servers has been devised by Marie 2°, and this will form the basis of the approximation method used here. Before its use is described some properties of closed queueing networks with nonexponential servers will be examined. In open queueing systems, service-time variability and interarrival-time variability at a server both tend to increase queue length 21,22. The most obvious instance in which this occurs is the M/G/1 queue (see, for example, Reference 23). In a closed queueing system, queue lengths need not increase with the service time variance. It has been observed 12,24 that the queue length at the bottleneck server, i.e. the one with the highest utilization, may decrease as the service time variance is increased. The reason is that increasing the service-time variance at the bottleneck causes its interdeparture time variability to increase far more than it would at less loaded servers. Because increasing the interdeparture time variability at one server tends to increase the interarrival time variability and queue length at the others, jobs are drawn away from
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the bottleneck. Since the network population is fixed, the queue length at the bottleneck decreases. This effect has been called the bottleneck anomaly 12'24. The effect is pronounced in closed queueing networks in which the bottleneck server is highly variable and heavily loaded. However, although service time variability affects queue lengths to a certain extent, it degrades performance far less in networks with fixed numbers of jobs than it does in open queueing systems in which the number of jobs is unbounded. The author has proposed an approach to the problem of combining LAN and host models where the LAN is a token ring11'12. The network is alternately treated as a server in a model of the host and as an open queue fed by a set of external Poisson arrival processes whose rates correspond to the traffic offered by each host. Each host treated as a central server model 13 with the LAN gateway acting as a peripheral server (see Figure I). The models are disjoint in the sense that jobs do not migrate from one host to another. Each host is treated as a self-contained unit, with a fixed population and its own workload characteristics. Its LAN gateway is treated as a (possibly) nonexponential server whose mean is the time taken to transmit the packet. The 'apparent' coefficient of variation (CV) of the nonexponential server reflects the variability of the blocking delay due to other hosts. The gateway server's apparent CV is fitted by: • Step A: determining how many packets would be queued at each host if the LAN were modelled as an open system, • Step B: replacing the gateway server at each host with a nonexponential server having the same queue length, given its arrival rate, • Step C: using Marie's algorithm 2° for closed queueing systems with nonexponential servers to solve the resulting model of each host in turn. Because the waiting times and queue lengths produced by the token-ring model are used to compute the apparent CVs of the gateway servers in the host models, and because the apparent CVs are needed to compute the packet arrival rates of the ring by host, the two models must be run alternately, so that each can provide the inputs necessary for the other. The iterations are started by running the host models with zero service times at the gateway servers, which yields throughputs that are used as inputs to the token-ring model. The process is repeated until the outputs of successive iterations are sufficiently close. This procedure is described in detail in Reference 11. Step A is performed using a previously validated open queueing model of the LAN and the assumption that arrivals are Poisson. Formally, let ik denote the server index of the LAN port at host k. Let Xik,k = 1 . . . . . n denote the packet arrival rate at the I_AN port of the kth host. Let Sik denote the packet transmission time at the kth host. Let WL(k)(Xil, Xi2 ..... Xin, Sik) denote the waiting time of a packet there, as predicted by an open queue model. Typically, the Sik s are identical at all hosts, i.e. for all k. Step B is performed by equating the queue lengths derived from Step A with the Pollacek-Khinchine formula for an M/G/1 queue at each host and solving for the
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'apparent' service time CV. The apparent CV of the kth LAN post server, Cik may be obtained by solving
Pik2(1 uc Cik 2) 2Xik(1 -- Pik)
-- WL(k)(Xil , Xi 2 .....
Xi n, Si k)
where Pik denotes the utilization of the LAN by the kth host. Once the Cik s have been obtained, an iteration of Marie's algorithm may be performed for each host to obtain better estimates of its performance measures, including the throughputs used as parameters for the open LAN models. The purpose of Step C is twofold. First, Marie's algorithm fits a state-dependent arrival process to each server. Since no arrivals occur when all jobs are queued at the gateway, this procedure counteracts the error of assuming infinite arrival streams in Steps A and B. The state-dependent arrival process also captures the effect of interarrival variability on the queue length of the station. Second, the effect of interdeparture time variability at the gateway is propagated throughout the network model of each host, because the nonexponential server is treated as load dependent when it forms part of the complementary networks of the other servers at the host. The algorithm is summarized in Figure 2. For token rings with equal arrival rates at all stations, Takagi's exact model may be used to obtain values for the Wt(k)S8. For token rings with unequal arrival rates at the stations and fixed packet lengths, approximate models have been described by Kuehn~6, Berry and Chandy 19and Boxma and Meister 24.An exact model for token rings with unequal arrival rates is difficult to obtain, perhaps because the embedded Markov chain at token arrival instants is periodic when the packet queue length at each host is bounded 11. The proposed model integration algorithm is selfcorrecting: in the event that the hosts generate packets at a rate that saturates the LAN, the apparent CVs of the port servers will be large enough to reduce the predicted throughputs, and hence the apparent service time CVs, at the end of the next iteration.
LAN Model Integration Algorithm: Estimate throughput at each gateway (decomposition at each host);
repeat Determine resultant waiting time at all gateways using open model, current estimate of throughputs; Fit 'apparent CVs' from (1), Coxian distributions to gateways; Run one Marie iteration for each host, yielding new estimate of throughputs and queue lengths; Apply Marie's corrections to each host if needed; until Marie's convergence criterion satisfied at each host.
Figure 2. Proposed algorithm for integrating gateway model into host models computer communications
The method of apparent CVs has been successfully used to model the effect of contention for a token ring on the performance of individual hosts 11' 25. Its predictions have been compared with simulation results for a wide range of model parameters, including systems with hosts having very different workload characteristics 11. The method may be used to model the sharing of a resource by two or more otherwise disjoint closed queueing systems.
because the size of the state space increases exponentially with the number of job classes. The cost of solving models of systems with large numbers of job classes is high even with the Recal algorithm, the cost of which is polynomial in the number of jobs classes27. By contrast, the cost of each iteration of the apparent CVs method is quadratic in the total number of jobs at all hosts. However, the number of iterations depends on the required accuracy of convergence and on the workload. Moreover, convergence of the iterative procedure is not guaranteed.
Processor-sharing model of token-ring contention A server is said to have a processor-sharing (PS) discipline if the rate at which service is delivered decreases in proportion to the number of jobs present, i.e. if the average service rate is la, it is IJ/n if n jobs are present. The PS discipline may be thought of as the limit of a roundrobin discipline, as the size of the time slice tends to zero. During presentations of the work in the previous section, the author has been asked about the possibility of treating the token ring as a PS server with a menu service time equal to the transmission time, because the nonexhaustive service discipline is approximately equivalent to time slicing. Each host would be treated as a job class, the members of which would not visit servers at the other hosts, as shown in Figure 3. The token ring server would be visited by all job classes. The numerical results in Tables 1-3 show that this method works well when the the hosts have identical workloads but fails otherwise. The reason for the failure in the asymmetrical case is that the processor-sharing method implicitly ignores the ability of the cyclic nonexhaustive service discipline to prevent a very active host from depriving all others of network access 26. Instead, it treats all queued jobs in exactly the same manner. Note that if the PSserver has an exponential service time distribution with the same mean for all job classes, the response time is exactly the same as for a FCFS server 19. The processor-sharing model is computationally intractable for networks with a large number of hosts, Host 0
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Modelling the network A host may transmit on an Ethernet whenever it is idle. Unlike the token ring, the Ethernet has no access control mechanism other than collision detection. The Ethernet may be modelled as a load-dependent server, the rate of which depends on the number of hosts attempting to transmit simultaneously 2' 28. A global view of the Ethernet is shown in Figure 4. The hosts alternate between processing (thinking or quiescent) and attempting to transmit. When they are attempting to transmit, they may be regarded as queueing for the Ethernet server marked Enet. When they are processing, they reside at the delay server Hosts, the think time of which is the time between packet generations. The number of jobs in the network is equal to the number of hosts. This approach has also been used to model a Cambridge ring 1°. The parameters of the load-dependent server are expressed in terms of the efficiency of the Ethernet, which depends on collision probabilities, the number of hosts attempting to transmit and the maximum bit rate. Collision-resolution policies are not taken into account in this model. The load-dependent modelling technique has been used by Lazowska et al) 8 to model the performance of a network consisting of a file server and a number of discless client stations. It is assumed that there is only one user per client station and that all clients are identical. The user process migrate from the client CPU to the file server via the LAN whenever disc I/O is performed. The user process returns to the client CPU via the LAN when I/O is complete. The client stations are modelled as pure delay
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MODELLING ETHERNET CONTENTION USING LOAD-DEPENDENT SERVERS
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Figure 3. Processor sharing model of a token ring connected to two hosts; solid lines represent the path followed by jobs at HostO, dotted lines the path at Host1. ~ - - I FSFSserver, Eli:__] PS server
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Figure 4. Global model of hosts connected to an EtherneL .F~7~ load-dependent server, 0 delay (IS) server
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servers, the file server CPU and disc are modelled as FCFS servers, and the Ethernet connecting them is modelled as a load-dependent server. There is only one process per client, and that process migrates; the model shown in Figure 5 is thus obtained. The population of the network is equal to the number of client stations. The model should be accurate as long as the LAN utilization is low. Lazowska et al. have used this model to argue that a network of discless workstations is more cost effective then a network of hard-disc stations in a software development environment. In the systems they studied, Ethernet contention rarely exceeded 10%. There is, however, a potential source of error in their model: processes that are returning from the file server to their home bases all queue at the server marked Enet in Figure 5, but the number in this queue represents the number of processors that cause collisions. Since only the first job in the actual file server transmission queue causes a collision, predictions about Ethernet contention may be somewhat pessimistic.
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Figure 5. Single-user client workstations connected to a file server; dashed lines represent the return path of a job from the file server to its client CPU. I J FCFS server, load- dependent server, O delay (IS) server
Table 1. Symmetrical network model: comparison of predicted values, simulation means and 95% confidence limits for Station 0 Server name
Visit ratio
Service time
Service time CV
124.00 45.00 3.00 75.00
0.0030 0.0150 0.0450 0.0012
1.0 1.0 1.0 0.0
Parameters CPU Disc1 Disc2 Gate Server
MACV
PS
Sim. Mean
St. Dev
Lower CL
Upper CL
Utilizations CPU Disc1 Disc2 Gate
0.5162 0.9367 0.1873 0.1211
0.5154 0.9352 0.1870 0.1247
0.5223 0.9009 0.1961 0.1165
0.0064 0.1277 0.0142 0.0006
0.5105 0.6664 0.1701 0.1154
0.5342 1.1354 0.2221 0.1175
0.9038 2.7317 0.2259 0.1386
0.8999 2.7111 0.2254 0.1636
0.9056 2.7170 0.2338 0.1401
0.0300 0.0380 0.0322 0.0013
0.8506 2.6472 0.1747 0.1377
0.9607 2.7868 0.2929 0.1424
172.0780 62.4477 4.1632 104.0793
171.8081 62.3497 4.1566 103.9162
172.7375 62.6500 4.1735 104.5450
0.8610 0.4519 0.0592 0.4999
171.1558 61.8198 4.0648 103.6267
174.3192 63.4802 4.2822 105.4633
0.0053 0.0437 0.0543 0.0013
0.0052 0.0435 0.0542 0.0016
0.0052 0.0386 0.0573 0.0013
0.0002 0.0168 0.0045 0.0000
0.0049 0.0076 0.0489 0.0013
0.0056 0.0695 0.0656 0.0014
Queue lengths CPU Disc1 Disc2 Gate
Throughputs CPU Disc1 Disc2 Gate
Response times CPU Disc1 Disc2 Gate
MACV: Method of apparentCVs PS: Processor-sharingmodel Ring loading approximately 25% All serversexponential exceptthe ring
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However, the impact of this error should be small as long as the LAN is lightly loaded.
Extensions The model described above is applicable to systems with one process per client host. We shall now consider how client hosts that have more than one user logged in can be modelled. This method has not been validated. However, it is based on techniques that have been successfully used in other applications "9' 30. The method is presented with a view to conveying a flavour of how approximation methods might be put together. Since there is more than one job per client host, movement to the gateway server cannot be equated with a transmission attempt. To do so would induce the sort of error mentioned in connection with a file-server transmission in the previous subsection. Contention at the
client CPUs and at the client discs, if any, must also be modelled. The system will be decomposed into a set of submodels; one for each client host, one for the LAN and one for the file server, as shown in Figures 6-8. Each of the submodels requires input parameters that are outputs of the others, so some iteration is required. For a discussion of iterative approximation methods, see Reference 2. The LAN is modelled as a multiple-class closed system, as shown in Figure 7. As in Figure 4, the Ethernet is modelled as the load-dependent server marked Enet. Each job class corresponds to a type of host (file server or client) with a population (MPL) equal to the number of hosts of each type. The file server model is shown in Figure 6. The client server model is shown in Figure 8. Within the LAN model, each host is modelled as an infinite server, which is visited only by jobs of the corresponding class. Each client host model contains a dummy FCFSserver representing the transmission queue approaching the
Table 2. Asymmetrical network model: comparison of predicted values, simulation means and 95% confidence limits for Host 0 Server name
Visit ratio
Service time
Service time CV
114.00 I 0.00 3.00 100.00
0.0030 0.0150 0.0150 0.0012
1.0 1.0 1.0 0.0
Parameters CPUI Discl Disc2 Gate
Server
MACV
PS
Sire. Mean
St. Dev
Lower CL
Upper CL
Utilizations CPU1 Disc1 Disc2 Gate
0.9528 0.4179 0.1254 0.3199
0.9398 0.4122 0.1237 0.3297
0.9581 0.4126 0.1279 0.3116
0.0063 0.0263 0.0166 0.0063
0.9465 0.3644 0.0974 0.3000
0.9698 0.4608 0.1584 0.3232
2.8010 0.6499 0.1417 0.4071
2.7101 0.6355 0.1395 0.5149
2.8063 0.6366 0.1433 0.4138
0.0694 0.0560 0.0190 0.0017
2.6787 0.5337 0.1083 0.4107
2.9338 0.7396 0.1782 0.4168
317.6102 27.8605 8.3582 278.6113
313.2608 27.4790 8.2437 274.7902
317.8250 27.1000 8.0765 279.5750
5.0265 0.2287 0.4261 5.6486
308.5908 26.6799 7.2937 269.1978
0.0088 0.0233 0.0170 0.0015
0.0087 0.0231 0.0169 0.0019
0.0088 0.0235 0.0178 0.0015
0.0003 0.0021 0.0024 0.0000
0.0083 0.0196 0.0133 0.0014
Queue lengths CPU1 Disc1 Disc2 Gate
Throughputs CPU1 Disc1 Disc2 Gate
327.0592 27.5201 8.8593 289.9522
Response times CPU1 Disc1 Disc2 Gate
0.0094 0.0274 0.0222 0.0015
MACV: Method of apparent CVs PS: Processor-sharing model
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I.AN access gateway. The service time at the gateway server is equal to the response time of Enet in the LAN submodel, because this is the time taken for a packet to be transmitted once it has reached the head of the transmission queue. Task migration to the file server is modelled by the delay server FS,the service time of which is the time it takes the file server to process a request and send it back again. The population of the client host is equal to the number of users logged in. The file server model is similar to the client host models. It contains a dummy FCFSserver representing the I_AN access gateway. It also contains a delay server representing the time a client process spends away from the file server before returning with another request. The population of the file server is equal to the sum of the populations of the client hosts. As with the token ring model, it is necessary to iterate between the three submodels, because each has parameters that are outputs of the others. For instance, the
client host model contains server FS, which is the time spent by an enquiry at the file server. This in turn is an output of the file server model, which takes the response times of the client servers as parameters.
DISCUSSION OF THE MODELLING APPROACHES The token ring and Ethernet incorporation approaches discussed above are similar in that each method splits the system model into a set of submodels, each of which requires inputs from the others to make performance predictions. However, the approaches differ in a number of respects. The token ring model assumes that tasks remain at their native hosts and do not migrate from one host to another. It also assumes that jobs return to their respective CPUs once packet transmission has been completed, rather than move into a suspended state while waiting for
Table 3. Asymmetrical network model: comparison of predicted values, simulation means and 95% confidence limits for Host 1 Server name
Visit ratio
Service time
Service time CV
121.00 50.00 20.00 50.00
0.0030 0.0150 0.0150 0.0012
1.0 1.0 1.0 0.0
Parameters CPU1 Disc1 Disc2 Gate Server
MACV
PS
Sim. mean
St Dev
Lower CL
Upper CL
Utilizations CPU1 Disc1 Disc2 Gate
0.3334 0.6888 0.8265 0.0533
0.4490 0.9277 0.3711 0.0742
0.3474 0.7019 0.8303 0.0533
0.0306 0.0800 0.0510 0.0057
0.2911 0.5549 0.7366 0.0429
0.4036 0.8490 0.9240 0.0638
0.4662 1.4407 2.0299 0.0632
0.1203 0.7198 2.6154 0.1203
0.4892 1.4595 1.9835 0.0678
0.0488 0.2680 0.2938 0.0075
0.3994 0.9671 1.4438 0.0540
0.5789 1.9519 2.5232 0.0816
111.1246 45.9193 18.3677 45.9193
149.6641 61.8447 24.7379 61.8447
114.6750 47.0625 18.8100 47.8350
9.8633 3.4813 1.6898 5.1001
96.5548 40.6670 15.7056 38.4655
132.7952 53.4580 21.9144 57.2045
0.0042 0.0314 0.1105 0.0014
0.0048 0.0423 0.0220 0.0019
0.0043 0.0310 0.1058 0.0014
0.0001 0.0043 0.0200 0.0000
0.0040 0.0231 0.0690 0.0014
0.0045 0.0389 0.1426 0.0014
Queue lengths CPU 1 Disc1 Disc2 Gate
Throughputs CPU1 Disc1 Disc2 Gate
Response times CPU1 Disc1 Disc2 Gate
MACV: Method of apparent CVs PS: Processor-sharing model
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computer communications
FS-Disc
FS-CPU
]
FS-Gate
Figure 6. File server submodel for system with multiple I FCFS server, users logged into each client CPU. r o delay (IS) server
I
z
7
=1 Enet l - Figure Z Ethemet submodel for client serves connected to a local host. FS denotes a file server, CLS denotes a set of client servers. ~ load-dependent server, O delay (IS) server Client server . .
~ . ~
CL-Disc01~
Figure 8. Client s e r v e r submodel with contention: FS denotes the file server. I - - ] FCFS server, © d e l a y (IS) s e r v e r a response from a remote machine. The effect of task migration or suspension of execution could be modelled in this framework by creating dummy delay servers in each host model to represent the times during which jobs do not compete for local resources. This is precisely the approach that the present authors have taken in the model of the network with multiple jobs at each client host. The two approaches also differ in the same manner in which I_AN contention has been treated. As the shortcomings of the processor-sharing model have already been discussed, only the method of apparent CVs will be considered here. The approach taken in this method is to match the variance of the packet transmission time in the
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host models to the apparent variance of the service time in the I_AN model. This enables the effect of unequal packet arrival rates on the network blocking to be taken into account in the host model. It also means that the utilization of the gateway server in the host model is equal to the proportion of time that the ring is dedicated to the associated host. A deficiency of this approach is that the variance of the service time at the gateway is fitted heuristically. Ideally, some means should be found to account for both mean and the variance of the network blocking delay in the model. This is the subject of future research. The approach taken in the Ethernet models is to characterize LAN contention in terms of the number of hosts competing for the network at any instant. This model is a faithful representation of the access method and has been applied successfully. The discussion in the previous section suggests that the method must be applied with care, lest the effects of asymmetrical Ioadings induce spurious predictions at heavy loads. The choice of method for predicting the effect of Ethernet contention on host performance is influenced by the observation that the network blocking delay depends both on the number of hosts attempting to gain access simultaneously and on the total offered load. The utilization of the network is predicted by the network submodel. Utilization of the dummy gateway servers in the host models corresponds to the proportion time that at least one packet is undergoing a network access delay, including transmission time.
CONCLUSIONS
Modelling LAN contention and its effect on host computers is complicated because LAN access methods are difficult to model precisely and because the workload at each host influences the performance of the others. The poor performance of the processor shared token ring model shows that even the simplest model can contain pitfalls that lead to inaccurate performance predictions. The modeller must also decide whether to treat each host as a self-contained unit or to take the effect of task migration into account. Modelling methods that attempt to address each of these concerns have been presented. Each method incorporates aspects that capture some aspect of system behaviour while neglecting others. A key to the development of a successful model is the ability to recognize those aspects of a system that should be incorporated and those details that can be neglected because their complexity contributes little to the accuracy of the predictions.
A C K N O W L E D G E M ENTS
The work on the method of apparent CVs was performed at Purdue University as part of the author's doctoral research. Computing facilities at Purdue were provided by the Department of Computer Science and the Purdue
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University Computing Center. Simulations were performed using the SLAM programming language31. The author wishes to thank his major professor, Peter J Denning, for his advice and encouragement during the course of this work. The processor-sharing model of token ring contention was suggested independently by Herb Schwetman and Thien Vo Dai, following oral presentations of this work at Purdue University and at the Performance 84 conference respectively. While preparing this paper, the author exchanged electronic correspondence with Ed Lazowska, whose comments on the approach to modelling Ethemet and the proposed extensions were exceedingly helpful.
REFERENCES 1 Schoch, I R and Hupp, I A'Measured performance of an Ethernet local network' Commun. ACM Vo123 No 12 (1980) pp 711-720 2 Lazowska, E D et al. Quantitative system performance: computer system analysis using queueing network models Prentice Hall, USA (1984) 3 Sauer, C H and Chandy, K M Computer systems performance modeling Prentice Hall, USA (1981) 4 Ferrari, D Computersystems performance evaluation Prentice Hall, USA (1978) 5 Bard, Y 'A model of shared DASD and multipathing' Commun. ACM Vol 23 No 10 (1980) pp 564-583 6 Bard,Y '1/0 systems with dynamic path selection and general transmission networks' Proc. ACM Sigmetrics (Perf. EvaL Rev.) Vol 11 No 4 (1982) pp 118-129 7 Bux, W e t al. A reliable token-ring system for localarea communication IBM Research Report No RZ 1095 (#39517), IBM Zurich Laboratory, Rueschlikon Switzerland (9 March 1981) 8 Salwen, H On ring architected local neworks Proteon Report, Proteon Associates, USA (April 1982) 9 Metcalfe, R M and Boggs, D Ethernet: distributed packet switching for local computer networks Report CSL-75-7, Xerox PARC, USA (1975) 10 Bux, W 'Local area subnetworks: a performance comparison' IEEE Trans. Commun. Vol COM-29 No 10 (1981) pp 1645-1673 11 Bondi, A B 'Modeling the effect of local area network contention on the performance of host computers' Proc. Performance '84, IFIP Working Group 7.3 Paris, France (December 1984) pp 303-320 12 Bondi, A B Incorporating open queueing models into closed queueing network algorithms PhD Thesis, Purdue University, USA (May 1984) 13 Buzen, I P 'Computational algorithms for closed queueing networks with exponential servers' Commun. ACM Vol 16 No 9 (1973) pp 527-531 14 Reiser, M and Lavenberg, S S 'Mean value analysis of closed multichain queueing networks' J. Assoc. CompuL Mach. Vol 27 No 2 (1980) pp 313-322 15 Bruell, S C and Balbo, G Computational algorithms for closed queueing networks North Holland, USA (I 980)
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16 King, P J B and Mitrani, I 'Modeling the Cambridge ring' Proc. ACM Sigmetrics Perf. Eval. Rev. Vol 11 No 4 (1982) pp 250-258 17 Lunn, K and Bennett, L 'Message transport in the Cambridge ring: a simulation study' Software PracL & Exper. Vol 11 No 7 (1981) pp 711-716 18 Lazowska, E D et al. 'File access performance of discless workstations' Trans. CompuL SysL Vol 4 No 3 (1986) pp 238-268 19 Baskett, F et al. 'Open, closed, and mixed networks of queues with different classes of customers' J. Assoc. CompuL Mach. Vol 22 No 2 (1975) pp 248-260 20 Marie, R 'Methodes iteratives de resolution de modeles mathematiques de systemes informatiques' RAIRO informatique/computer science Vol 12 No 2 (1978) 21 Whitt, W 'The queueing network analyser' Bell Syst. Tech. J. Vol 62 No 9 (1983) pp 2779-2816 22 Whirl, W 'Performance of the queueing network analyser' Bell. SysL Tech. J. Vol 62 No 9 (1983) pp 2817-2844 23 Cox, D R and Smith, W I. Queues Methuen, UK (1961) 24 Bondi, A B and Whitt, W 'The effects of service time variability in a closed network of queues' Perf. Eval. Vol 6 No 3 (1986) pp 219-234 25 Berry, R and Chandy, K M 'Performance models of token ring local area networks' Proc. ACM Sigmetrics Conf. (1983) pp 266-274 26 Kuehn, P l 'Multiqueue systems with non-exhaustive cyclic service' Bell Syst Tech. J. (1979) pp 671-698 27 Conway, A E and Georganas, N D Recah a new efficient algorithm for the exact analysis of multiplechain closed queueing networks IN RIA, Rocquen court (March 1985) 28 Almes, G T and Lazowska, E D The behaviour of Ethernet-like computer communications networks Technical Report No 79-05-01, Dept. of Computer Science, University of Washington, USA (April 1979) 29 Lazowska, E D and Zahorjan, I 'Multiple class memory constrained queueing networks' Proc. ACM Sigmetrics Conf. Measure. & Model. CompuL SysL (1982) pp 130-140 30 Zahorjan, J 'The influence of workload representation on response times in queueing models of computer systems' Proc. ACM Sigmetrics Conf. (1983) pp 70-81 31 Pritsker, A A B and Pegden, C D Introduction to simulation and SLAM,Halsted Press, USA (1979)
BIBLIOGRAPHY Boxma, O J and Meister, B Waiting-time approximations for cyclic service systems with switch-over times IBM Research Report RZ 1449 (#52543) IBM Zurich Laboratory, Rueschlikon, Switzerland (February 1986) Takagi, H 'Mean message waiting times in a symmetric polling system' in Gelenbe, E (Ed.) Proc. Performance '84, Paris North Holland, The Netherlands (1984) computer communications
Networks consisting of special-purpose workstations connected by local area networks have become very popular. Their use may grow to the point where LAN contention degrades the performance of the application, e.g. in graphics workstations whose images must be updated frequently or in applications involving large file transfers. Methods of predicting the level of I_ANcontention and its effect on host performance are discussed, and the way in which this problem affects token rings and CSMAtype networks is examined. Keywords: computer networks, performance, LAN contention, token ring networks, CSMA networks, mathematical modelling
In recent years, it has become economically feasible to connect several workstations, mainframe, mini and personal computers via a local area network (LAN). Many minicomputers have speeds similar to those of mainframes, but because they are often running only a few jobs at a time, they are able to offer traffic to the LAN at rates that may be considerably higher than those offered by mainframes, which may be executing many jobs concurrently. In addition, minicomputers may support applications such as file transfers and high-speed image Department of Computer Science,University of California,SantaBarbara, CA 93106, USA
processing, which require the movement of large volumes of data and have stringent timing constraints. It is therefore likely that LAN utilization may exceed the low levels (less than 10%) reported in Reference I. Reasonable network access times may not be feasible at utilizations as low as 30% on some network media; on CSMA-type networks, for instance, access times escalate even at moderate loads because of repeated collisions. Of course, the load offered to a LAN depends on the rate at which hosts can generate packets for transmission. This depends not only on the processing requirements of higher level protocols, but also on the usage of the CPU and I/O devices at each host. Only the latter usage is considered here. If the CPU is heavily loaded by application work, packets may not be generated fast enough to cause severe network contention. On the other hand, if the CPU is moderately loaded and the application requires that repeated enquiries be made of a remote file server, the network loading may be substantial. This paper discusses techniques for predicting LAN loading in terms of the workloads at individual host computers. The techniques presented here may also be used to analyse such problems as file placement on workstations, file servers and conventional mainframes. Lazowska et al., 2 Sauer and Chandy3 and Ferrari4 have discussed the relevant performance-evaluation techniques. In systems in which packet generation corresponds to I/0, the process that generates a packet may be blocked until transmission has been completed. Consequently, network contention may have a detrimental effect on host performance. The problem of modelling such
0140-3664/87/020070-09 $03.00 © 1987 Butterworth & Co (Publishers) Ltd 70
computer communications
systems is similar to that of modellinga disc shared by two or more CPUs s' 6, because the load offered to the network by each host influences the performance of the other hosts. A shared disc with a single path may be modelled as a server which is accessed via a FCFSqueue common to all of the conneced CPUs. The problem is more complicated for LANs, because hosts do not usually access the network in an order susceptible to analytical modelling such as FCFS, processor sharing, or pure delay (infinite service). For instance, token rings such as the Zurich rings and ProNet 7' 8 and CSMA buses like Ethernet9 have very different access methods and consequently have different performance characteristics under light and heavy loads 1°. The token rings use the nonexhaustive service discipline, i.e. each host is allowed to transmit at most one packet during every complete cycle of the token. With Ethernet, all stations may attempt to transmit at any time. If two or more attempt transmission simultaneously, they must back off for random intervals and try to transmit again. These characteristics must be taken into account when formulating a performance model of the entire system N' 12. Rather than developing entirely new tools to address the problem, a system of hosts will be decomposed into separate units, each of which will be modelled using wellknown queueing network algorithms for obtaining performance measures such as those described in References 2 and 13-15. These algorithms may be combined with LAN models to produce a model of the complete system. Two modelling approaches will be examined. The first approach 11'12 is applicable to networks in which the media access mechanism selects hosts to transmit data in turn, such as the Zurich and ProNet rings7' 8. The second approach 2'16 is applicable to contention-based access mechanisms such as CSMA 9 and slotted rings such as the Cambridge ring 17. In both of these, the network access discipline is symmetrical in the sense that the medium can be acquired immediately if it is available. The second approach has been successfully used by Lazowska et al. to model a system consisting of single-user workstations connected to a file server via an Ethernet18. Both approaches will be analysed and the merits and deficiencies of each will be discussed. Some extensions will also be proposed. It should be emphasized that the extensions have not been validated against either live or simulated data. However, they are presented in order to give the reader a flavour of some possible approaches to model development.
MODELLING A TOKEN RING'S IMPACT ON HOST'S PERFORMANCE Method of apparent coefficients of variation ALAN may be regarded as a device that is accessed via a gateway attached to each of the host computers it connects. In the absence of buffering, a job will move to its host's gateway every time it generates a packet and then return to the CPU once transmission of the packet is
vol 10 no 2 april 1987
oil0\
HostO
ILl
CPUO
i I
~
I I I
Gate~ Disc1
H ~ o s t l CPU1
Disc12
Figure 1. Token ring connected to two hosts; represents the model used in the method of apparent coefficients of variation: Z ~ FCFS server, ®/_AN, discipline unspecified complete, as illustrated in Figure 1. In this respect, a gateway is no different from the secondary storage device in the central server model 13. However, the waiting time of a job at the gateway is influenced not only by the workload characteristics of the host, but also by the traffic at other hosts. It follows that the network access delay at one host depends on the workload characteristics of the other hosts and vice versa. A packet may spend time at the head of a gateway dispatch queue without actually receiving service. This time will be termed the packet blocking delay. The distribution of the packet blocking delay is not exponential in general. This violates one of the basic assumptions of closed queueing network models solvable by exact methods 19. However, a fast method for solving closed queueing network models with nonexponential servers has been devised by Marie 2°, and this will form the basis of the approximation method used here. Before its use is described some properties of closed queueing networks with nonexponential servers will be examined. In open queueing systems, service-time variability and interarrival-time variability at a server both tend to increase queue length 21,22. The most obvious instance in which this occurs is the M/G/1 queue (see, for example, Reference 23). In a closed queueing system, queue lengths need not increase with the service time variance. It has been observed 12,24 that the queue length at the bottleneck server, i.e. the one with the highest utilization, may decrease as the service time variance is increased. The reason is that increasing the service-time variance at the bottleneck causes its interdeparture time variability to increase far more than it would at less loaded servers. Because increasing the interdeparture time variability at one server tends to increase the interarrival time variability and queue length at the others, jobs are drawn away from
71
the bottleneck. Since the network population is fixed, the queue length at the bottleneck decreases. This effect has been called the bottleneck anomaly 12'24. The effect is pronounced in closed queueing networks in which the bottleneck server is highly variable and heavily loaded. However, although service time variability affects queue lengths to a certain extent, it degrades performance far less in networks with fixed numbers of jobs than it does in open queueing systems in which the number of jobs is unbounded. The author has proposed an approach to the problem of combining LAN and host models where the LAN is a token ring11'12. The network is alternately treated as a server in a model of the host and as an open queue fed by a set of external Poisson arrival processes whose rates correspond to the traffic offered by each host. Each host treated as a central server model 13 with the LAN gateway acting as a peripheral server (see Figure I). The models are disjoint in the sense that jobs do not migrate from one host to another. Each host is treated as a self-contained unit, with a fixed population and its own workload characteristics. Its LAN gateway is treated as a (possibly) nonexponential server whose mean is the time taken to transmit the packet. The 'apparent' coefficient of variation (CV) of the nonexponential server reflects the variability of the blocking delay due to other hosts. The gateway server's apparent CV is fitted by: • Step A: determining how many packets would be queued at each host if the LAN were modelled as an open system, • Step B: replacing the gateway server at each host with a nonexponential server having the same queue length, given its arrival rate, • Step C: using Marie's algorithm 2° for closed queueing systems with nonexponential servers to solve the resulting model of each host in turn. Because the waiting times and queue lengths produced by the token-ring model are used to compute the apparent CVs of the gateway servers in the host models, and because the apparent CVs are needed to compute the packet arrival rates of the ring by host, the two models must be run alternately, so that each can provide the inputs necessary for the other. The iterations are started by running the host models with zero service times at the gateway servers, which yields throughputs that are used as inputs to the token-ring model. The process is repeated until the outputs of successive iterations are sufficiently close. This procedure is described in detail in Reference 11. Step A is performed using a previously validated open queueing model of the LAN and the assumption that arrivals are Poisson. Formally, let ik denote the server index of the LAN port at host k. Let Xik,k = 1 . . . . . n denote the packet arrival rate at the I_AN port of the kth host. Let Sik denote the packet transmission time at the kth host. Let WL(k)(Xil, Xi2 ..... Xin, Sik) denote the waiting time of a packet there, as predicted by an open queue model. Typically, the Sik s are identical at all hosts, i.e. for all k. Step B is performed by equating the queue lengths derived from Step A with the Pollacek-Khinchine formula for an M/G/1 queue at each host and solving for the
72
'apparent' service time CV. The apparent CV of the kth LAN post server, Cik may be obtained by solving
Pik2(1 uc Cik 2) 2Xik(1 -- Pik)
-- WL(k)(Xil , Xi 2 .....
Xi n, Si k)
where Pik denotes the utilization of the LAN by the kth host. Once the Cik s have been obtained, an iteration of Marie's algorithm may be performed for each host to obtain better estimates of its performance measures, including the throughputs used as parameters for the open LAN models. The purpose of Step C is twofold. First, Marie's algorithm fits a state-dependent arrival process to each server. Since no arrivals occur when all jobs are queued at the gateway, this procedure counteracts the error of assuming infinite arrival streams in Steps A and B. The state-dependent arrival process also captures the effect of interarrival variability on the queue length of the station. Second, the effect of interdeparture time variability at the gateway is propagated throughout the network model of each host, because the nonexponential server is treated as load dependent when it forms part of the complementary networks of the other servers at the host. The algorithm is summarized in Figure 2. For token rings with equal arrival rates at all stations, Takagi's exact model may be used to obtain values for the Wt(k)S8. For token rings with unequal arrival rates at the stations and fixed packet lengths, approximate models have been described by Kuehn~6, Berry and Chandy 19and Boxma and Meister 24.An exact model for token rings with unequal arrival rates is difficult to obtain, perhaps because the embedded Markov chain at token arrival instants is periodic when the packet queue length at each host is bounded 11. The proposed model integration algorithm is selfcorrecting: in the event that the hosts generate packets at a rate that saturates the LAN, the apparent CVs of the port servers will be large enough to reduce the predicted throughputs, and hence the apparent service time CVs, at the end of the next iteration.
LAN Model Integration Algorithm: Estimate throughput at each gateway (decomposition at each host);
repeat Determine resultant waiting time at all gateways using open model, current estimate of throughputs; Fit 'apparent CVs' from (1), Coxian distributions to gateways; Run one Marie iteration for each host, yielding new estimate of throughputs and queue lengths; Apply Marie's corrections to each host if needed; until Marie's convergence criterion satisfied at each host.
Figure 2. Proposed algorithm for integrating gateway model into host models computer communications
The method of apparent CVs has been successfully used to model the effect of contention for a token ring on the performance of individual hosts 11' 25. Its predictions have been compared with simulation results for a wide range of model parameters, including systems with hosts having very different workload characteristics 11. The method may be used to model the sharing of a resource by two or more otherwise disjoint closed queueing systems.
because the size of the state space increases exponentially with the number of job classes. The cost of solving models of systems with large numbers of job classes is high even with the Recal algorithm, the cost of which is polynomial in the number of jobs classes27. By contrast, the cost of each iteration of the apparent CVs method is quadratic in the total number of jobs at all hosts. However, the number of iterations depends on the required accuracy of convergence and on the workload. Moreover, convergence of the iterative procedure is not guaranteed.
Processor-sharing model of token-ring contention A server is said to have a processor-sharing (PS) discipline if the rate at which service is delivered decreases in proportion to the number of jobs present, i.e. if the average service rate is la, it is IJ/n if n jobs are present. The PS discipline may be thought of as the limit of a roundrobin discipline, as the size of the time slice tends to zero. During presentations of the work in the previous section, the author has been asked about the possibility of treating the token ring as a PS server with a menu service time equal to the transmission time, because the nonexhaustive service discipline is approximately equivalent to time slicing. Each host would be treated as a job class, the members of which would not visit servers at the other hosts, as shown in Figure 3. The token ring server would be visited by all job classes. The numerical results in Tables 1-3 show that this method works well when the the hosts have identical workloads but fails otherwise. The reason for the failure in the asymmetrical case is that the processor-sharing method implicitly ignores the ability of the cyclic nonexhaustive service discipline to prevent a very active host from depriving all others of network access 26. Instead, it treats all queued jobs in exactly the same manner. Note that if the PSserver has an exponential service time distribution with the same mean for all job classes, the response time is exactly the same as for a FCFS server 19. The processor-sharing model is computationally intractable for networks with a large number of hosts, Host 0
q
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Modelling the network A host may transmit on an Ethernet whenever it is idle. Unlike the token ring, the Ethernet has no access control mechanism other than collision detection. The Ethernet may be modelled as a load-dependent server, the rate of which depends on the number of hosts attempting to transmit simultaneously 2' 28. A global view of the Ethernet is shown in Figure 4. The hosts alternate between processing (thinking or quiescent) and attempting to transmit. When they are attempting to transmit, they may be regarded as queueing for the Ethernet server marked Enet. When they are processing, they reside at the delay server Hosts, the think time of which is the time between packet generations. The number of jobs in the network is equal to the number of hosts. This approach has also been used to model a Cambridge ring 1°. The parameters of the load-dependent server are expressed in terms of the efficiency of the Ethernet, which depends on collision probabilities, the number of hosts attempting to transmit and the maximum bit rate. Collision-resolution policies are not taken into account in this model. The load-dependent modelling technique has been used by Lazowska et al) 8 to model the performance of a network consisting of a file server and a number of discless client stations. It is assumed that there is only one user per client station and that all clients are identical. The user process migrate from the client CPU to the file server via the LAN whenever disc I/O is performed. The user process returns to the client CPU via the LAN when I/O is complete. The client stations are modelled as pure delay
....
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MODELLING ETHERNET CONTENTION USING LOAD-DEPENDENT SERVERS
I"
L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Figure 3. Processor sharing model of a token ring connected to two hosts; solid lines represent the path followed by jobs at HostO, dotted lines the path at Host1. ~ - - I FSFSserver, Eli:__] PS server
vol 10 no 2 april 1987
J
Figure 4. Global model of hosts connected to an EtherneL .F~7~ load-dependent server, 0 delay (IS) server
73
servers, the file server CPU and disc are modelled as FCFS servers, and the Ethernet connecting them is modelled as a load-dependent server. There is only one process per client, and that process migrates; the model shown in Figure 5 is thus obtained. The population of the network is equal to the number of client stations. The model should be accurate as long as the LAN utilization is low. Lazowska et al. have used this model to argue that a network of discless workstations is more cost effective then a network of hard-disc stations in a software development environment. In the systems they studied, Ethernet contention rarely exceeded 10%. There is, however, a potential source of error in their model: processes that are returning from the file server to their home bases all queue at the server marked Enet in Figure 5, but the number in this queue represents the number of processors that cause collisions. Since only the first job in the actual file server transmission queue causes a collision, predictions about Ethernet contention may be somewhat pessimistic.
\) !
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Figure 5. Single-user client workstations connected to a file server; dashed lines represent the return path of a job from the file server to its client CPU. I J FCFS server, load- dependent server, O delay (IS) server
Table 1. Symmetrical network model: comparison of predicted values, simulation means and 95% confidence limits for Station 0 Server name
Visit ratio
Service time
Service time CV
124.00 45.00 3.00 75.00
0.0030 0.0150 0.0450 0.0012
1.0 1.0 1.0 0.0
Parameters CPU Disc1 Disc2 Gate Server
MACV
PS
Sim. Mean
St. Dev
Lower CL
Upper CL
Utilizations CPU Disc1 Disc2 Gate
0.5162 0.9367 0.1873 0.1211
0.5154 0.9352 0.1870 0.1247
0.5223 0.9009 0.1961 0.1165
0.0064 0.1277 0.0142 0.0006
0.5105 0.6664 0.1701 0.1154
0.5342 1.1354 0.2221 0.1175
0.9038 2.7317 0.2259 0.1386
0.8999 2.7111 0.2254 0.1636
0.9056 2.7170 0.2338 0.1401
0.0300 0.0380 0.0322 0.0013
0.8506 2.6472 0.1747 0.1377
0.9607 2.7868 0.2929 0.1424
172.0780 62.4477 4.1632 104.0793
171.8081 62.3497 4.1566 103.9162
172.7375 62.6500 4.1735 104.5450
0.8610 0.4519 0.0592 0.4999
171.1558 61.8198 4.0648 103.6267
174.3192 63.4802 4.2822 105.4633
0.0053 0.0437 0.0543 0.0013
0.0052 0.0435 0.0542 0.0016
0.0052 0.0386 0.0573 0.0013
0.0002 0.0168 0.0045 0.0000
0.0049 0.0076 0.0489 0.0013
0.0056 0.0695 0.0656 0.0014
Queue lengths CPU Disc1 Disc2 Gate
Throughputs CPU Disc1 Disc2 Gate
Response times CPU Disc1 Disc2 Gate
MACV: Method of apparentCVs PS: Processor-sharingmodel Ring loading approximately 25% All serversexponential exceptthe ring
74
computer communications
However, the impact of this error should be small as long as the LAN is lightly loaded.
Extensions The model described above is applicable to systems with one process per client host. We shall now consider how client hosts that have more than one user logged in can be modelled. This method has not been validated. However, it is based on techniques that have been successfully used in other applications "9' 30. The method is presented with a view to conveying a flavour of how approximation methods might be put together. Since there is more than one job per client host, movement to the gateway server cannot be equated with a transmission attempt. To do so would induce the sort of error mentioned in connection with a file-server transmission in the previous subsection. Contention at the
client CPUs and at the client discs, if any, must also be modelled. The system will be decomposed into a set of submodels; one for each client host, one for the LAN and one for the file server, as shown in Figures 6-8. Each of the submodels requires input parameters that are outputs of the others, so some iteration is required. For a discussion of iterative approximation methods, see Reference 2. The LAN is modelled as a multiple-class closed system, as shown in Figure 7. As in Figure 4, the Ethernet is modelled as the load-dependent server marked Enet. Each job class corresponds to a type of host (file server or client) with a population (MPL) equal to the number of hosts of each type. The file server model is shown in Figure 6. The client server model is shown in Figure 8. Within the LAN model, each host is modelled as an infinite server, which is visited only by jobs of the corresponding class. Each client host model contains a dummy FCFSserver representing the transmission queue approaching the
Table 2. Asymmetrical network model: comparison of predicted values, simulation means and 95% confidence limits for Host 0 Server name
Visit ratio
Service time
Service time CV
114.00 I 0.00 3.00 100.00
0.0030 0.0150 0.0150 0.0012
1.0 1.0 1.0 0.0
Parameters CPUI Discl Disc2 Gate
Server
MACV
PS
Sire. Mean
St. Dev
Lower CL
Upper CL
Utilizations CPU1 Disc1 Disc2 Gate
0.9528 0.4179 0.1254 0.3199
0.9398 0.4122 0.1237 0.3297
0.9581 0.4126 0.1279 0.3116
0.0063 0.0263 0.0166 0.0063
0.9465 0.3644 0.0974 0.3000
0.9698 0.4608 0.1584 0.3232
2.8010 0.6499 0.1417 0.4071
2.7101 0.6355 0.1395 0.5149
2.8063 0.6366 0.1433 0.4138
0.0694 0.0560 0.0190 0.0017
2.6787 0.5337 0.1083 0.4107
2.9338 0.7396 0.1782 0.4168
317.6102 27.8605 8.3582 278.6113
313.2608 27.4790 8.2437 274.7902
317.8250 27.1000 8.0765 279.5750
5.0265 0.2287 0.4261 5.6486
308.5908 26.6799 7.2937 269.1978
0.0088 0.0233 0.0170 0.0015
0.0087 0.0231 0.0169 0.0019
0.0088 0.0235 0.0178 0.0015
0.0003 0.0021 0.0024 0.0000
0.0083 0.0196 0.0133 0.0014
Queue lengths CPU1 Disc1 Disc2 Gate
Throughputs CPU1 Disc1 Disc2 Gate
327.0592 27.5201 8.8593 289.9522
Response times CPU1 Disc1 Disc2 Gate
0.0094 0.0274 0.0222 0.0015
MACV: Method of apparent CVs PS: Processor-sharing model
vol 10 no 2 april 1987
75
I.AN access gateway. The service time at the gateway server is equal to the response time of Enet in the LAN submodel, because this is the time taken for a packet to be transmitted once it has reached the head of the transmission queue. Task migration to the file server is modelled by the delay server FS,the service time of which is the time it takes the file server to process a request and send it back again. The population of the client host is equal to the number of users logged in. The file server model is similar to the client host models. It contains a dummy FCFSserver representing the I_AN access gateway. It also contains a delay server representing the time a client process spends away from the file server before returning with another request. The population of the file server is equal to the sum of the populations of the client hosts. As with the token ring model, it is necessary to iterate between the three submodels, because each has parameters that are outputs of the others. For instance, the
client host model contains server FS, which is the time spent by an enquiry at the file server. This in turn is an output of the file server model, which takes the response times of the client servers as parameters.
DISCUSSION OF THE MODELLING APPROACHES The token ring and Ethernet incorporation approaches discussed above are similar in that each method splits the system model into a set of submodels, each of which requires inputs from the others to make performance predictions. However, the approaches differ in a number of respects. The token ring model assumes that tasks remain at their native hosts and do not migrate from one host to another. It also assumes that jobs return to their respective CPUs once packet transmission has been completed, rather than move into a suspended state while waiting for
Table 3. Asymmetrical network model: comparison of predicted values, simulation means and 95% confidence limits for Host 1 Server name
Visit ratio
Service time
Service time CV
121.00 50.00 20.00 50.00
0.0030 0.0150 0.0150 0.0012
1.0 1.0 1.0 0.0
Parameters CPU1 Disc1 Disc2 Gate Server
MACV
PS
Sim. mean
St Dev
Lower CL
Upper CL
Utilizations CPU1 Disc1 Disc2 Gate
0.3334 0.6888 0.8265 0.0533
0.4490 0.9277 0.3711 0.0742
0.3474 0.7019 0.8303 0.0533
0.0306 0.0800 0.0510 0.0057
0.2911 0.5549 0.7366 0.0429
0.4036 0.8490 0.9240 0.0638
0.4662 1.4407 2.0299 0.0632
0.1203 0.7198 2.6154 0.1203
0.4892 1.4595 1.9835 0.0678
0.0488 0.2680 0.2938 0.0075
0.3994 0.9671 1.4438 0.0540
0.5789 1.9519 2.5232 0.0816
111.1246 45.9193 18.3677 45.9193
149.6641 61.8447 24.7379 61.8447
114.6750 47.0625 18.8100 47.8350
9.8633 3.4813 1.6898 5.1001
96.5548 40.6670 15.7056 38.4655
132.7952 53.4580 21.9144 57.2045
0.0042 0.0314 0.1105 0.0014
0.0048 0.0423 0.0220 0.0019
0.0043 0.0310 0.1058 0.0014
0.0001 0.0043 0.0200 0.0000
0.0040 0.0231 0.0690 0.0014
0.0045 0.0389 0.1426 0.0014
Queue lengths CPU 1 Disc1 Disc2 Gate
Throughputs CPU1 Disc1 Disc2 Gate
Response times CPU1 Disc1 Disc2 Gate
MACV: Method of apparent CVs PS: Processor-sharing model
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computer communications
FS-Disc
FS-CPU
]
FS-Gate
Figure 6. File server submodel for system with multiple I FCFS server, users logged into each client CPU. r o delay (IS) server
I
z
7
=1 Enet l - Figure Z Ethemet submodel for client serves connected to a local host. FS denotes a file server, CLS denotes a set of client servers. ~ load-dependent server, O delay (IS) server Client server . .
~ . ~
CL-Disc01~
Figure 8. Client s e r v e r submodel with contention: FS denotes the file server. I - - ] FCFS server, © d e l a y (IS) s e r v e r a response from a remote machine. The effect of task migration or suspension of execution could be modelled in this framework by creating dummy delay servers in each host model to represent the times during which jobs do not compete for local resources. This is precisely the approach that the present authors have taken in the model of the network with multiple jobs at each client host. The two approaches also differ in the same manner in which I_AN contention has been treated. As the shortcomings of the processor-sharing model have already been discussed, only the method of apparent CVs will be considered here. The approach taken in this method is to match the variance of the packet transmission time in the
vol 10 no 2 april 1987
host models to the apparent variance of the service time in the I_AN model. This enables the effect of unequal packet arrival rates on the network blocking to be taken into account in the host model. It also means that the utilization of the gateway server in the host model is equal to the proportion of time that the ring is dedicated to the associated host. A deficiency of this approach is that the variance of the service time at the gateway is fitted heuristically. Ideally, some means should be found to account for both mean and the variance of the network blocking delay in the model. This is the subject of future research. The approach taken in the Ethernet models is to characterize LAN contention in terms of the number of hosts competing for the network at any instant. This model is a faithful representation of the access method and has been applied successfully. The discussion in the previous section suggests that the method must be applied with care, lest the effects of asymmetrical Ioadings induce spurious predictions at heavy loads. The choice of method for predicting the effect of Ethernet contention on host performance is influenced by the observation that the network blocking delay depends both on the number of hosts attempting to gain access simultaneously and on the total offered load. The utilization of the network is predicted by the network submodel. Utilization of the dummy gateway servers in the host models corresponds to the proportion time that at least one packet is undergoing a network access delay, including transmission time.
CONCLUSIONS
Modelling LAN contention and its effect on host computers is complicated because LAN access methods are difficult to model precisely and because the workload at each host influences the performance of the others. The poor performance of the processor shared token ring model shows that even the simplest model can contain pitfalls that lead to inaccurate performance predictions. The modeller must also decide whether to treat each host as a self-contained unit or to take the effect of task migration into account. Modelling methods that attempt to address each of these concerns have been presented. Each method incorporates aspects that capture some aspect of system behaviour while neglecting others. A key to the development of a successful model is the ability to recognize those aspects of a system that should be incorporated and those details that can be neglected because their complexity contributes little to the accuracy of the predictions.
A C K N O W L E D G E M ENTS
The work on the method of apparent CVs was performed at Purdue University as part of the author's doctoral research. Computing facilities at Purdue were provided by the Department of Computer Science and the Purdue
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University Computing Center. Simulations were performed using the SLAM programming language31. The author wishes to thank his major professor, Peter J Denning, for his advice and encouragement during the course of this work. The processor-sharing model of token ring contention was suggested independently by Herb Schwetman and Thien Vo Dai, following oral presentations of this work at Purdue University and at the Performance 84 conference respectively. While preparing this paper, the author exchanged electronic correspondence with Ed Lazowska, whose comments on the approach to modelling Ethemet and the proposed extensions were exceedingly helpful.
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16 King, P J B and Mitrani, I 'Modeling the Cambridge ring' Proc. ACM Sigmetrics Perf. Eval. Rev. Vol 11 No 4 (1982) pp 250-258 17 Lunn, K and Bennett, L 'Message transport in the Cambridge ring: a simulation study' Software PracL & Exper. Vol 11 No 7 (1981) pp 711-716 18 Lazowska, E D et al. 'File access performance of discless workstations' Trans. CompuL SysL Vol 4 No 3 (1986) pp 238-268 19 Baskett, F et al. 'Open, closed, and mixed networks of queues with different classes of customers' J. Assoc. CompuL Mach. Vol 22 No 2 (1975) pp 248-260 20 Marie, R 'Methodes iteratives de resolution de modeles mathematiques de systemes informatiques' RAIRO informatique/computer science Vol 12 No 2 (1978) 21 Whitt, W 'The queueing network analyser' Bell Syst. Tech. J. Vol 62 No 9 (1983) pp 2779-2816 22 Whirl, W 'Performance of the queueing network analyser' Bell. SysL Tech. J. Vol 62 No 9 (1983) pp 2817-2844 23 Cox, D R and Smith, W I. Queues Methuen, UK (1961) 24 Bondi, A B and Whitt, W 'The effects of service time variability in a closed network of queues' Perf. Eval. Vol 6 No 3 (1986) pp 219-234 25 Berry, R and Chandy, K M 'Performance models of token ring local area networks' Proc. ACM Sigmetrics Conf. (1983) pp 266-274 26 Kuehn, P l 'Multiqueue systems with non-exhaustive cyclic service' Bell Syst Tech. J. (1979) pp 671-698 27 Conway, A E and Georganas, N D Recah a new efficient algorithm for the exact analysis of multiplechain closed queueing networks IN RIA, Rocquen court (March 1985) 28 Almes, G T and Lazowska, E D The behaviour of Ethernet-like computer communications networks Technical Report No 79-05-01, Dept. of Computer Science, University of Washington, USA (April 1979) 29 Lazowska, E D and Zahorjan, I 'Multiple class memory constrained queueing networks' Proc. ACM Sigmetrics Conf. Measure. & Model. CompuL SysL (1982) pp 130-140 30 Zahorjan, J 'The influence of workload representation on response times in queueing models of computer systems' Proc. ACM Sigmetrics Conf. (1983) pp 70-81 31 Pritsker, A A B and Pegden, C D Introduction to simulation and SLAM,Halsted Press, USA (1979)
BIBLIOGRAPHY Boxma, O J and Meister, B Waiting-time approximations for cyclic service systems with switch-over times IBM Research Report RZ 1449 (#52543) IBM Zurich Laboratory, Rueschlikon, Switzerland (February 1986) Takagi, H 'Mean message waiting times in a symmetric polling system' in Gelenbe, E (Ed.) Proc. Performance '84, Paris North Holland, The Netherlands (1984) computer communications