- Email: [email protected]
End-to-end performance of interconnected LANs
performance analysis
End-to-end performance of interconnected LANs Using the Mean Value Analysis method, Brigitte Berg and Robert H Deng propose an iterative algorithm to calculate the end-to-end performance of single-chain and multiple-chain closed queueing networks
The end-to-end performance of interconnected local area networks (LAN) is studied. The system uses bridges to connect distributed tANs through a high-speed communication link. The interconnected system is modelled as a single-chain and multiple-chain closed queueing system. Based on the MVA (mean value analysis) method, an iterative algorithm is proposed to calculate the end-to-end performance (intra-LAN and inter-LAN throughput and average message delays). The impacts of various system parameters such as window size, bridge processing time and the communication link capacity on the end-to-end performance, are investigated. Finally, the analytical results are verified by computer simulations. Keywords: performance, interconnected LANs, mean value analysis, computer simulation
Local area networks (LAN) offer high-speed communication between distributed system components, such as workstations and shared resources. Whenever the limitations of a single I_AN are reached with respect to the maximum number of attachments or maximum distance, means to interconnect LANs become necessary1. In this paper we consider the interconnection of two token-passing LANs depicted in Figure 1, where the interconnection is accomplished by connecting the LANs, through two bridges, to a high-speed and low error rate communication link. There are two types of traffic in the above interInstitute of Systems Science, National University of Singapore, Singapore 0511 March
Paperreceived:22
1990.Revisedpaperreceived:30June1990
connected system. Those messages which originate from one LAN and are destined for the other LAN are called inter-tAN messages, while those which are transmitted over the same I_AN are called intra-tAN messages. Bridges play an important role in handling the inter-LAN traffic. The basic functions of the bridge are summarized in the following2-4: 1 It reads all successfully transmitted messages on the LAN it is attached to, and accepts all the inter-LAN messages whose final destination is on the other LAN. 2 It relays inter-LAN messages to the bridge of the other LAN viathe bridge-to-bridge communication (intemet) link. 3 It broadcasts inter-I_AN messages received from the remote bridge to the workstations of its own LAN. Various performance studies have been conducted for the interconnected LAN similar to the one described above (see, for example, References 2 and 5). Most of the studies were concerned with the system performance at the lower layers in the context of the OSI seven-layer reference model. However, a good performance at the lower layers is only the first step towards high-speed endto-end communications. The overhead and processing delays of the higher layer protocols may significantly
~ Figure 1.
e Interconnected I_AN system
0140-3664/91/002105-08 © 1991 Butterworth-Heinemann Ltd vol 14 no 2 march 1991
105
performance analysis reduce the network transmission capacity that can be utilized by applications. The objective of this study was to develop a systematic model and its solution method with which we could study the end-to-end performance effects of the interconnected system protocol, bridge processing power and internet link capacity. The organization of the paper is as follows. We first provide a brief description on the protocol structure of the interconnected system, then we present the end-to-end performance model for the internetwork. The MVA (mean value analysis) methods for solving single-chain and multiple-chain closed queueing networks are described, and an iterative algorithgm for the solution of the end-to-end performance model that has been constructed is outlined. Numerical results obtained from the analysis are shown, and are compared with simulations. The impacts of various system parameters on the end-to-end performance are discussed.
Applicotion
Tronsport
LLC
INTERNETWORK END-TO-END PERFORMANCE MODEL Here we present the end-to-end performance queueing model for the internetwork. In building our model, we follow the approach used by Murata and Takagi6, where they introduce a two-layer model for token-passing rings. Figure 2 shows the layered protocol structure used in the internetwork. Application programs on workstations communicate with each other through three layers, i.e. the transport layer, the LLC (logical link control) layer and the MAC (media access control) layer. The MAC layer employs a token-passing protocol with limited service. The LLC layer provides two types of services to the layer above it, connection oriented services and connectionless services. In this study we only consider connectionless service for the LLC layer. The connectionless service is a datagram-style of service. It simply allows for sending and receiving fully addressed datagrams, with no form of acknowledgement to assure reliable delivery. The responsibilities of error recovery, flow control and resequencing of messages are left to the connectionoriented transport layer protocol.
MAC
PHY
Figure 2.
Pi
I_AN protocol structure
= ~.ihi,
(1)
i = 1,2 . . . . . N
The total utilization of the server is then given by: N
P= E
Pi
(2)
i=1
Modelling of the token-passing MAC layer The queueing model of the token-passing MAC layer is shown in Figure 3. The server (token) serves N MAC queues (stations and the bridge) in a cyclic manner. The service discipline is limited service (limited-to-one), which is the standard protocol adopted by IEEE 802.57. M essages arrl"ve at the i th MAC queue according to the Poisson process at a rate ~,i, i = 1, 2. . . . . N. Service times of messages at the/th MAC queue are independent and identically distributed (lid) random variables with first and second moments denoted by h i and h! 2), respectively. The walking times between consecutive stations are lid random variables with mean r and variance 6 2. The utilization of the server at the ith queue is defined as:
106
This paper deals only with the steady state of the system.
.
J
o
X2
x~ /= I, 2,.....,/V
Figure 3.
III1
o
Queueing, model of the token-passing MAC layer
computer communications
performance analysis It was shown by Kuehn 8 that the following conditions are necessary and sufficient for stability of the token-passing system: p < 1 and max(2i)Nr < 1 - p
1 -p+pi
Transport
LL:aO-"
Transpod
- ~--~(>--MAC MAC
042~ Transport
LLC
LLC
.~
AP
O-E:---O-E~ Transport
a
[~lTro~port
1 -p
1 - p - ~,i r
Station/
(3)
Exact analysis of such a system is an extremely complicated mathematical problem which has not been solved so far, except for the symmetrical system. However, various approximate results are available for the mean message waiting time for the above model. We use the approximation derived by Boxma and Meister9 which has been shown to be very close to computer simulations. The mean message waiting time at the i th queue is given byg: W i --
Stohon/
_...Z]:El==:~,z~
LAN I
[~Tronsport
N
(1 - p)p + i=1
N
P 2(1 - p)
j=l
Np6 2
+
Jhl2
b
N
r
2---r--+ 2(1
rronspor~
p~
Figure 4. End-to-end queueing model of the intemetwork (a) the intra-LAN submodel; (b) the inter-I.AN submodel
Pi(1 + Pi),
i=1 i = 1,2 . . . . . N
(4)
Then the total average message delay (the sum of the message waiting time, the message transmission time and the propagation time between sender i and a randomly selected receiver) at the i th MAC-queue is given by: fi = wi + hi + Nr/2,
i = 1,2 . . . . . N
(5)
Modelling of end-to-end connections We assume that the connection-oriented transport protocol operates a window-flow control-to-control message flow over a virtual channel/connection between a designated pair of stations. Each virtual channel has a source and a sink. The virtual channel has a maximum window size. Messages on a virtual channel are individually acknowledged via message piggyback mechanism. Throughout this paper, we assume that each station can only establish a single connection with another station. The above assumptions lead to the end-to-end queueing model of the internetwork shown in Figure 4. Figure 4a shows the submodel for intra-LAN connection between a pair of stations. The intra-LAN connection is modelled as a multiple-chain closed queueing network. The following features and assumptions are included in our model: 1 No message fragmentation and reassembly take place throughout the entire transmission process of a message. 2 The service time AP of the source corresponds to the interarrival time of messages which an application program at the source station can generate, and a
vol 14 no 2 march 1991
message is generated at the source only if an acknowledgement is received and processed by the source transport layer. This is to ensure that the number of messages and the acknowledgements on a chain be equal to its assigned window size. Since data message piggyback acknowledgements are used, the service time at the sink station corresponds to the interarrival time of the messages generated by the application program at the sink station. Both the source-queue and the sink-queue are modelled as IS (infinite servers) with service time AP. 3 The LLC layer and the transport layer are modelled by FCFS queues, respectively, with service times at both sending and receiving sides corresponding to the message processing times at the respective layers. 4 The chains interact with each other in the MAC layer. The MAC layer is modelled as IS with service time given by equation (5). Moreover, the inter-LAN connection model in Figure 4b has the following additional features: 1 All the inter-I_AN communication chains pass the two bridges and share the same internetwork link. The intemetwork link is full duplex capable of handling inter-I_AN traffic from both directions. 2 The bridging function at the bridge is modelled as a FCFS queue with service time BP respresenting the bridge processing time. 3 The intemetwork link is modelled as a FCFSqueue with service time LT corresponding to the link transmission time. The propagation delay LP between the two bridges is modelled as IS with service time equal to LP.
107
performance analysis SOLUTION ALGORITHM TO THE END-TO-END PERFORMANCE MODEL
It(W): ((W):
There exist many algorithms for solving the single-chain and multiple-chain closed queueing networks given in Figures 4a and 4b I°. Of particular interest to us is the MVA method presented by Reiser11. The MVA solution is exact when all FCFS queues in the closed network have exponentially distributed service times. When this is not the case, however, the MVA provides only approximate solutions.
throughput of chain r. mean queueing time of chain r messages at queue j.
Then it follows from Reiser11 that:
fi i for given r, j = MAC queue ~ j = AP or LP queue ~(w) =
z-~ [1 + n[ (W r - 1)] ifj = transport or LLC queue R
r)" [1 + ~
nk(W
-
er)]
if j = BP or LT queue
k=l
MVA algorithm for the single-chain queueing network
~r(w) -
Define for q u e u e j in the single-chain network of Figure 4a the following equilibrium quantities: W : chain population, i.e. the window size of the chain. ~-i : mean service time. ni(W): mean queue length including message in service. ti(W) : mean queueing time including message service time. t ( W ) : throughput of the chain. Then from Reiser11 it follows that: ~, = fi if queue j = MAC queue at station i ti(WI = ci if queue j = AP queue (6) ~i[1 + n j ( W - 1)] if queue j = Transport or LLC queue W
t(W) -
~.
(7)
j C- Q(r)
n~(W) = I r ( w ) ~(W)
(11 )
where W - er = (W 1. . . . . W r - 1, W r _ 1, W r + 1. . . . . wR).
Solution algorithm for the performance model In the above MVA algorithms, f/s obtained from equation (5) are used as the service times for the MAC queues. In turn, the 1's obtained from the MVA algorithms can be used as input values in equation (5) for those MAC queues which correspond to source or sink stations. In equation (5), the arrival rate to the bridge MAC queue and the first and second moments of the message service times at the bridge MAC queue are given by:
MW) '~"i = ~
ni(W) = ,t(W) ti(W)
(8)
where Q is the set of queues in the closed chain. Murata and Takagi 6 obtain fi from equation (5) for the MAC layer. Equations (6) to (8) can be solved recursively, starting with nj(O) = 0 for all j.
MVA algorithm for the multiple-chain queueing network We now extend our solution method to the multiplechain queueing network of Figure 4b. For this network we define the following notations: number of chains in the closed network (i.e. number of inter-bAN connections between source/sink pairs). W ~ : w i n d o w size of chain r, r = I, 2 . . . . . R. W : w i n d o w size vector, which is (W I . . . . . W R) Q(r) : set of queues in chain r. t-~" : mean service time of chain r messages at queue j. n~(W): mean number of chain r messages waiting and being served at queue j.
108
(10)
kE
and:
R
wr
:
~ r(W)
(I 2)
r=l
I
R
hi = ~11" ~ " "2Lr(W)hr r=l R
1
(13)
(14) r=l
The above observations leads us to an iterative solution algorithm, similar to the one presented by Murata and Takagi 6 for the end-to-end performance model. Therefore, we only outline the algorithm as follows: I Set arrival rates i i to the MAC layer to some initial values. 2 Check l i ' s with the stability condition (3). If condition (3) is not satisfied, then modify the arrival rates small enough to meet the stability condition and calculate f/ using equation (5). 3 Calculate the throughput for each chain of Figures 4a and 4b using the corresponding MVA algorithms. These values will be used in the next iteration cycle as arrival rates tot he MAC layer. The iteration continues until the following convergence criterion is met:
computer communications
performance analysis N
4 The bridge processing time BP is assumed to be comparable with LLC processing time, and is I ms. 5 The internet link speed can be I Mbit/s, 0.67 Mbit/s, or 0.33 Mbit/s, which corresponds to mean message transmission time LT = 4 ms, 6 ms and 12 ms, respectively, for an average message size of 500 bytes. 6 Propagation delay LP between the two bridges is 0.05 ms.
an= i=I
where ~ < < 1 (e.g. ~
=
10-s).
NUMERICAL RESULTS AND DISCUSSION Here we present numerical results to demonstrate the end-to-end performance effects of network protocols (e.g. window size), bridge processing power and the internet link transmission capacity.
System configuration and parameters In all the numerical examples we consider the example internetwork depicted in Figure 5, where two identical token-rings are interconnected using bridges via the internetwork link. There are eight stations attached to each LAN. Among these eight stations, two stations communicate with the corresponding two stations of the other bAN, while the other six stations communicate among themselves over the same LAN, as depicted in Figure 5. In other words, the internetwork has two interbAN connections and three intra-LAN connections in each bAN. The following parameters are used for our numerical examples: I The bAN speed is kept constant at 4 Mbit/s. Message size follows the exponential distribution with an average length of 500 bytes. Then the message transmission time is also exponentially distributed with mean of h = I ms. 2 Walking time between adjacent stations (including station latency) is exponentially distributed with mean r = 0.005 ms. 3 Processing times per message at the LLC layer and the transport layer depend on the implementation of the protocols, the processor speed, buffer passing method, etc. We assume that processing times for LLC queues at both transmitting and receiving sides are 1 ms, and that processing times for transport queues at both transmitting and receiving sides are 6 ms 6' 12.
// / /
/
\\
C}x\
\ ~ /
j
,i, i I I C)"
\\C// Figure 5.
D"
Intemetwork used for numerical examples
vol 14 no 2 march 1991
I I
Numerical and simulation results We used the RESQ package 13 to simulate the internet of Figure5, where the two token rings are simulated according to the model given in Figure 3. Throughout the following examples, the simulation results are shown as 'o' and the numerical results are plotted by curves. We use the postfixes 'intra', 'inter' and %' to denote the system performance parameters related to intra-LAN connection, inter-LAN connection and the bridge, respectively. For example, W-intra and W-inter denote the window sizes for intra-LAN and inter-l_AN connections, respectively. Figures 6a and 6b show the internetwork performance for the case of W-intra--W-inter, LT = 4ms, and AP = 25 ms. Figure 6a shows the average delays at MAC queues, transport queues and the internetwork link queue. Average end-to-end delays for intra-bAN and inter-LAN connections are also shown in the figure. The throughput per intra-LAN and inter-bAN connection are plotted in Figure 6b. These figures indicate that numerical results are in good agreement with the simulation results. From Figure 6a we see that for small window sizes, the system bottlenecks are in the transport layer (as well as in the internetwork link for inter-bAN connections). As the window sizes reach such values that the system throughput becomes saturated (this happens in Figure 6b for window size larger than 12), the bottleneck shifts to the MAC layer. The influence of the message generation time AP on throughput is presented in Figure 7, where we compare the throughput for the cases of AP = 25, 50 and 100 ms. We note that by keeping W-intra = W-inter, the throughput per inter-LAN connection can never exceed the throughput per intra-bAN connection. Next, we demonstrate the effect of changing the window size W-inter. The average delays and throughput for the case with AP -- 50, LT = 6 ms, W-intra = 8 and Winter = 1,2 . . . . . 40 are shown in Figures8a and 8b, respectively. In this case, except for very small values of W-inter, the internetwork link is the bottleneck. This is true in almost all practical systems where the internetwork link capacity is smaller than the transmission capacity of the bANs. We observe that when W-intra is fixed, the throughput per inter-LAN connection can be varied by changing the window size W-inter, and it is possible for inter-bAN throughput to exceed the intra-LAN throughput (per connection), even with the internetwork link as the bottleneck. However, this situation will change when the transmission capacity of the internetwork link is reduced to a certain level, as shown in Figure 9, which gives the
109
performance analysis 200
0.12
Inter-LAN I00 0.10
Intro- LAN
%) End-to-end
0.08
Transport
8,
- inter
Transport - intra
=o
P
o.o6
Per intro-LAN connection
.E F-
IO
Per inter- LAN connection
0.04 MAC-b MAC -intro
Internetwork
link
0.02
MAC -inter
I.O " I 0 a
I
I
I
I IO
I
I
I
I
o 20
W - i n t r o , W - inter
I o
b
I
I
I
I I I0 w-intro, W-inter
I
I
I 20
Figure 6. (a) Average delays in the case with W-intra = W-inter, AP = 25 ms, LT = 4 ms; (b) Throughput in the case with W-intra = W-inter, AP = 25 ms, LT = 4 ms
o.12
0.i0-
i --.- . . . . /
16
/
/
/
/
0 08 -
J
/
/I
~
/
/
/
Z
:--
.,~.
/
system performance for the case with LT = 12 Ms, and with other system parameters the same as in Figure 8. In Figure 9, due to the increased link processing time, the inter-LAN throughput per connection is always less than the intra-LAN throughput per connection, no matter what values W-inter may take. The impact of the bridge processing time to the internetwork performance is similar to that of the internetwork link transmission capacity. Therefore, the corresponding curves are not included in this paper.
i 0.06 -
//
I-
CONCLUSION
AP:25 /
C' / o.o
-
o.o
_
/ /;P:50
,I///
/
. yAP=
I00
I
I
'/,/.y o
I
0
I
I
I
I0
I
I
20
W- intra, W- inter
Figure 7. Throughput comparison W-intra = W-inter, LT = 4 ms
1I 0
in the cases with
In this paper we have investigated the end-to-end performance of interconnected token-ring LAwNs. The end-to-end intra-LAN connections are modelled as a single-chain closed queueing network, while the end-toend inter-LAN connections are modelled as a multiplechain closed queueing network. The performance model of the system was solved by an iteration algorithm with the aid of the MVA method. Numerical examples and computer simulations were presented to show the performance characteristics of the interconnected system. Our results indicated that the transport layer window size, the bridge processing speed and the internet link speed have significant influences on the end-to-end inter-l_AN performance.
computer communications
performance analysis 0. I0 I000
inter- LAN
Intro-LAN
~__._._...~~
0.08
I00
0.06
I0 ~
~i
MAC-b
0
I I0
oo21
Transport -intro •
I 20 W-inter
a
Per intro- LAN connection
~- 0.04 nsport- inter
inter t
l
k link
MAC-intro I 30
I I0
0
40
b
] 20 W-inter
I 30
40
Figure 8. (a) Average delays in the case with AP = 50 ms, LT = 6 ms W-intra = 8, W-inter = 1,2. . . . . 40; (b) Throughput in the case with AP = 50 ms, LT = 6 ms W-intra = 8, W-inter = 1,2 . . . . . 40 0.10 Inter- LAN
IOOC
0 08
Per inter- LAN connection 0.06
I00
£ .c ~- 0 0 4
e
//•
MAC
002
Tronsport- inter
0
oo
I0
a
20
30
0
40
w-inter
Per intra- I_AN connection
1 tO
b
[ 20 W- inter
I 30
40
Figure 9. (a) Average delays in the case with AP = 50 ms, LT = 12 ms W-intra = 8, W-inter = 1,2 . . . . . 40; (b) Throughput in the case with AP = 50 ms, LT = 12 ms W-intra = 8, W-inter = 1,2. . . . . 40
There are some problems with such interconnected systems which need further investigation: I System performance in asymmetrical cases, e.g. the two token-rin~ have different configurations and characteristics. 2 System performance when the bridge has a higher priority than user stations. 3 System performance with server/client configuration (as in Murata and Takagi6).
ACKNOWLEDGEMENTS
REFERENCES 1 Kummerle, K, Limb, J O and Tabagi, F A (eds) Advances in Local Area Networks IEEEPress, NY, USA
(1987) 2 Exley, G M and Merakos, L F 'Throughput-delay performance of interconnected CSMA local area networks' IEEE J. Selected Areas in C o m m u n . Vol 5 No 9 (December 1987) pp 1380-1389 3 Tanenbaum, A S C o m p u t e r Networks (2nd edn) Prentice-Hall, NJ, USA (1988) 4 Hawe, B, Kirby, A and Stewart, B 'Transparent interconnection of local networks with bridges' in
Kummerle K, Limb, l O and Tabagi, F A (eds) The authors would like to thank the anonymous referees for their comments and suggestions on this paper.
vol 14 no 2 march 1991
Advances in Local Area Networks I EEE Press, NY, USA
(1987) pp 482-495
111
performance analysis 5 Heath, J R 'Analysis of gateway congestion in interconnected high-speed local networks' IEEE Trans. Commun. Vol36 No8 (August 1988) pp 986-989 6 Murata, M and Takagi, H 'Two-layer modelling for local area networks' IEEE Trans. Commun. Vol 36 No 9 (September 1988) pp 1022-1033 7 ANSI/IEEEStandard 802.5, Token RingAccess Method IEEE Press, NY, USA (1985) 8 Kuehn, P J 'Multiqueue system with non-exhaustive cyclic service' Bell 5ysL Tech. J. Vol 58 (1979) pp 671-698 9 Boxma, O J and Meister, B 'Waiting time approximations for cyclic-service systems with switchover times' Perf. Eval. Vol 7 (November 1987) pp 299-308
112
10 Zahorjan, J, Eager, D L and Sweillam, H M 'Accuracy, speed and convergence of approximate mean value analysis' Perf. EvaL (1988) pp 255-270 11 Reiser, M 'A queueing network analysis of computer communication networks with window flow control' IEEE Trans. Commun. Vol 27 (August 1979) pp 1199-1209 12 Meister, B W, Janson, P A and Svobodova, L 'Connection-oriented versus connectionless protocols: a performance study' IEEE Trans. Comput. Vol 34 (December 1985) pp 1164-1173 13 Sauer, C H, MacNair, S A and Kurose, l F The Research Queueing Package Version 2; Introduction and Examples IBM TJ Watson Research Center, NY, USA (April 1982)
computer communications
End-to-end performance of interconnected LANs Using the Mean Value Analysis method, Brigitte Berg and Robert H Deng propose an iterative algorithm to calculate the end-to-end performance of single-chain and multiple-chain closed queueing networks
The end-to-end performance of interconnected local area networks (LAN) is studied. The system uses bridges to connect distributed tANs through a high-speed communication link. The interconnected system is modelled as a single-chain and multiple-chain closed queueing system. Based on the MVA (mean value analysis) method, an iterative algorithm is proposed to calculate the end-to-end performance (intra-LAN and inter-LAN throughput and average message delays). The impacts of various system parameters such as window size, bridge processing time and the communication link capacity on the end-to-end performance, are investigated. Finally, the analytical results are verified by computer simulations. Keywords: performance, interconnected LANs, mean value analysis, computer simulation
Local area networks (LAN) offer high-speed communication between distributed system components, such as workstations and shared resources. Whenever the limitations of a single I_AN are reached with respect to the maximum number of attachments or maximum distance, means to interconnect LANs become necessary1. In this paper we consider the interconnection of two token-passing LANs depicted in Figure 1, where the interconnection is accomplished by connecting the LANs, through two bridges, to a high-speed and low error rate communication link. There are two types of traffic in the above interInstitute of Systems Science, National University of Singapore, Singapore 0511 March
Paperreceived:22
1990.Revisedpaperreceived:30June1990
connected system. Those messages which originate from one LAN and are destined for the other LAN are called inter-tAN messages, while those which are transmitted over the same I_AN are called intra-tAN messages. Bridges play an important role in handling the inter-LAN traffic. The basic functions of the bridge are summarized in the following2-4: 1 It reads all successfully transmitted messages on the LAN it is attached to, and accepts all the inter-LAN messages whose final destination is on the other LAN. 2 It relays inter-LAN messages to the bridge of the other LAN viathe bridge-to-bridge communication (intemet) link. 3 It broadcasts inter-I_AN messages received from the remote bridge to the workstations of its own LAN. Various performance studies have been conducted for the interconnected LAN similar to the one described above (see, for example, References 2 and 5). Most of the studies were concerned with the system performance at the lower layers in the context of the OSI seven-layer reference model. However, a good performance at the lower layers is only the first step towards high-speed endto-end communications. The overhead and processing delays of the higher layer protocols may significantly
~ Figure 1.
e Interconnected I_AN system
0140-3664/91/002105-08 © 1991 Butterworth-Heinemann Ltd vol 14 no 2 march 1991
105
performance analysis reduce the network transmission capacity that can be utilized by applications. The objective of this study was to develop a systematic model and its solution method with which we could study the end-to-end performance effects of the interconnected system protocol, bridge processing power and internet link capacity. The organization of the paper is as follows. We first provide a brief description on the protocol structure of the interconnected system, then we present the end-to-end performance model for the internetwork. The MVA (mean value analysis) methods for solving single-chain and multiple-chain closed queueing networks are described, and an iterative algorithgm for the solution of the end-to-end performance model that has been constructed is outlined. Numerical results obtained from the analysis are shown, and are compared with simulations. The impacts of various system parameters on the end-to-end performance are discussed.
Applicotion
Tronsport
LLC
INTERNETWORK END-TO-END PERFORMANCE MODEL Here we present the end-to-end performance queueing model for the internetwork. In building our model, we follow the approach used by Murata and Takagi6, where they introduce a two-layer model for token-passing rings. Figure 2 shows the layered protocol structure used in the internetwork. Application programs on workstations communicate with each other through three layers, i.e. the transport layer, the LLC (logical link control) layer and the MAC (media access control) layer. The MAC layer employs a token-passing protocol with limited service. The LLC layer provides two types of services to the layer above it, connection oriented services and connectionless services. In this study we only consider connectionless service for the LLC layer. The connectionless service is a datagram-style of service. It simply allows for sending and receiving fully addressed datagrams, with no form of acknowledgement to assure reliable delivery. The responsibilities of error recovery, flow control and resequencing of messages are left to the connectionoriented transport layer protocol.
MAC
PHY
Figure 2.
Pi
I_AN protocol structure
= ~.ihi,
(1)
i = 1,2 . . . . . N
The total utilization of the server is then given by: N
P= E
Pi
(2)
i=1
Modelling of the token-passing MAC layer The queueing model of the token-passing MAC layer is shown in Figure 3. The server (token) serves N MAC queues (stations and the bridge) in a cyclic manner. The service discipline is limited service (limited-to-one), which is the standard protocol adopted by IEEE 802.57. M essages arrl"ve at the i th MAC queue according to the Poisson process at a rate ~,i, i = 1, 2. . . . . N. Service times of messages at the/th MAC queue are independent and identically distributed (lid) random variables with first and second moments denoted by h i and h! 2), respectively. The walking times between consecutive stations are lid random variables with mean r and variance 6 2. The utilization of the server at the ith queue is defined as:
106
This paper deals only with the steady state of the system.
.
J
o
X2
x~ /= I, 2,.....,/V
Figure 3.
III1
o
Queueing, model of the token-passing MAC layer
computer communications
performance analysis It was shown by Kuehn 8 that the following conditions are necessary and sufficient for stability of the token-passing system: p < 1 and max(2i)Nr < 1 - p
1 -p+pi
Transport
LL:aO-"
Transpod
- ~--~(>--MAC MAC
042~ Transport
LLC
LLC
.~
AP
O-E:---O-E~ Transport
a
[~lTro~port
1 -p
1 - p - ~,i r
Station/
(3)
Exact analysis of such a system is an extremely complicated mathematical problem which has not been solved so far, except for the symmetrical system. However, various approximate results are available for the mean message waiting time for the above model. We use the approximation derived by Boxma and Meister9 which has been shown to be very close to computer simulations. The mean message waiting time at the i th queue is given byg: W i --
Stohon/
_...Z]:El==:~,z~
LAN I
[~Tronsport
N
(1 - p)p + i=1
N
P 2(1 - p)
j=l
Np6 2
+
Jhl2
b
N
r
2---r--+ 2(1
rronspor~
p~
Figure 4. End-to-end queueing model of the intemetwork (a) the intra-LAN submodel; (b) the inter-I.AN submodel
Pi(1 + Pi),
i=1 i = 1,2 . . . . . N
(4)
Then the total average message delay (the sum of the message waiting time, the message transmission time and the propagation time between sender i and a randomly selected receiver) at the i th MAC-queue is given by: fi = wi + hi + Nr/2,
i = 1,2 . . . . . N
(5)
Modelling of end-to-end connections We assume that the connection-oriented transport protocol operates a window-flow control-to-control message flow over a virtual channel/connection between a designated pair of stations. Each virtual channel has a source and a sink. The virtual channel has a maximum window size. Messages on a virtual channel are individually acknowledged via message piggyback mechanism. Throughout this paper, we assume that each station can only establish a single connection with another station. The above assumptions lead to the end-to-end queueing model of the internetwork shown in Figure 4. Figure 4a shows the submodel for intra-LAN connection between a pair of stations. The intra-LAN connection is modelled as a multiple-chain closed queueing network. The following features and assumptions are included in our model: 1 No message fragmentation and reassembly take place throughout the entire transmission process of a message. 2 The service time AP of the source corresponds to the interarrival time of messages which an application program at the source station can generate, and a
vol 14 no 2 march 1991
message is generated at the source only if an acknowledgement is received and processed by the source transport layer. This is to ensure that the number of messages and the acknowledgements on a chain be equal to its assigned window size. Since data message piggyback acknowledgements are used, the service time at the sink station corresponds to the interarrival time of the messages generated by the application program at the sink station. Both the source-queue and the sink-queue are modelled as IS (infinite servers) with service time AP. 3 The LLC layer and the transport layer are modelled by FCFS queues, respectively, with service times at both sending and receiving sides corresponding to the message processing times at the respective layers. 4 The chains interact with each other in the MAC layer. The MAC layer is modelled as IS with service time given by equation (5). Moreover, the inter-LAN connection model in Figure 4b has the following additional features: 1 All the inter-I_AN communication chains pass the two bridges and share the same internetwork link. The intemetwork link is full duplex capable of handling inter-I_AN traffic from both directions. 2 The bridging function at the bridge is modelled as a FCFS queue with service time BP respresenting the bridge processing time. 3 The intemetwork link is modelled as a FCFSqueue with service time LT corresponding to the link transmission time. The propagation delay LP between the two bridges is modelled as IS with service time equal to LP.
107
performance analysis SOLUTION ALGORITHM TO THE END-TO-END PERFORMANCE MODEL
It(W): ((W):
There exist many algorithms for solving the single-chain and multiple-chain closed queueing networks given in Figures 4a and 4b I°. Of particular interest to us is the MVA method presented by Reiser11. The MVA solution is exact when all FCFS queues in the closed network have exponentially distributed service times. When this is not the case, however, the MVA provides only approximate solutions.
throughput of chain r. mean queueing time of chain r messages at queue j.
Then it follows from Reiser11 that:
fi i for given r, j = MAC queue ~ j = AP or LP queue ~(w) =
z-~ [1 + n[ (W r - 1)] ifj = transport or LLC queue R
r)" [1 + ~
nk(W
-
er)]
if j = BP or LT queue
k=l
MVA algorithm for the single-chain queueing network
~r(w) -
Define for q u e u e j in the single-chain network of Figure 4a the following equilibrium quantities: W : chain population, i.e. the window size of the chain. ~-i : mean service time. ni(W): mean queue length including message in service. ti(W) : mean queueing time including message service time. t ( W ) : throughput of the chain. Then from Reiser11 it follows that: ~, = fi if queue j = MAC queue at station i ti(WI = ci if queue j = AP queue (6) ~i[1 + n j ( W - 1)] if queue j = Transport or LLC queue W
t(W) -
~.
(7)
j C- Q(r)
n~(W) = I r ( w ) ~(W)
(11 )
where W - er = (W 1. . . . . W r - 1, W r _ 1, W r + 1. . . . . wR).
Solution algorithm for the performance model In the above MVA algorithms, f/s obtained from equation (5) are used as the service times for the MAC queues. In turn, the 1's obtained from the MVA algorithms can be used as input values in equation (5) for those MAC queues which correspond to source or sink stations. In equation (5), the arrival rate to the bridge MAC queue and the first and second moments of the message service times at the bridge MAC queue are given by:
MW) '~"i = ~
ni(W) = ,t(W) ti(W)
(8)
where Q is the set of queues in the closed chain. Murata and Takagi 6 obtain fi from equation (5) for the MAC layer. Equations (6) to (8) can be solved recursively, starting with nj(O) = 0 for all j.
MVA algorithm for the multiple-chain queueing network We now extend our solution method to the multiplechain queueing network of Figure 4b. For this network we define the following notations: number of chains in the closed network (i.e. number of inter-bAN connections between source/sink pairs). W ~ : w i n d o w size of chain r, r = I, 2 . . . . . R. W : w i n d o w size vector, which is (W I . . . . . W R) Q(r) : set of queues in chain r. t-~" : mean service time of chain r messages at queue j. n~(W): mean number of chain r messages waiting and being served at queue j.
108
(10)
kE
and:
R
wr
:
~ r(W)
(I 2)
r=l
I
R
hi = ~11" ~ " "2Lr(W)hr r=l R
1
(13)
(14) r=l
The above observations leads us to an iterative solution algorithm, similar to the one presented by Murata and Takagi 6 for the end-to-end performance model. Therefore, we only outline the algorithm as follows: I Set arrival rates i i to the MAC layer to some initial values. 2 Check l i ' s with the stability condition (3). If condition (3) is not satisfied, then modify the arrival rates small enough to meet the stability condition and calculate f/ using equation (5). 3 Calculate the throughput for each chain of Figures 4a and 4b using the corresponding MVA algorithms. These values will be used in the next iteration cycle as arrival rates tot he MAC layer. The iteration continues until the following convergence criterion is met:
computer communications
performance analysis N
4 The bridge processing time BP is assumed to be comparable with LLC processing time, and is I ms. 5 The internet link speed can be I Mbit/s, 0.67 Mbit/s, or 0.33 Mbit/s, which corresponds to mean message transmission time LT = 4 ms, 6 ms and 12 ms, respectively, for an average message size of 500 bytes. 6 Propagation delay LP between the two bridges is 0.05 ms.
an= i=I
where ~ < < 1 (e.g. ~
=
10-s).
NUMERICAL RESULTS AND DISCUSSION Here we present numerical results to demonstrate the end-to-end performance effects of network protocols (e.g. window size), bridge processing power and the internet link transmission capacity.
System configuration and parameters In all the numerical examples we consider the example internetwork depicted in Figure 5, where two identical token-rings are interconnected using bridges via the internetwork link. There are eight stations attached to each LAN. Among these eight stations, two stations communicate with the corresponding two stations of the other bAN, while the other six stations communicate among themselves over the same LAN, as depicted in Figure 5. In other words, the internetwork has two interbAN connections and three intra-LAN connections in each bAN. The following parameters are used for our numerical examples: I The bAN speed is kept constant at 4 Mbit/s. Message size follows the exponential distribution with an average length of 500 bytes. Then the message transmission time is also exponentially distributed with mean of h = I ms. 2 Walking time between adjacent stations (including station latency) is exponentially distributed with mean r = 0.005 ms. 3 Processing times per message at the LLC layer and the transport layer depend on the implementation of the protocols, the processor speed, buffer passing method, etc. We assume that processing times for LLC queues at both transmitting and receiving sides are 1 ms, and that processing times for transport queues at both transmitting and receiving sides are 6 ms 6' 12.
// / /
/
\\
C}x\
\ ~ /
j
,i, i I I C)"
\\C// Figure 5.
D"
Intemetwork used for numerical examples
vol 14 no 2 march 1991
I I
Numerical and simulation results We used the RESQ package 13 to simulate the internet of Figure5, where the two token rings are simulated according to the model given in Figure 3. Throughout the following examples, the simulation results are shown as 'o' and the numerical results are plotted by curves. We use the postfixes 'intra', 'inter' and %' to denote the system performance parameters related to intra-LAN connection, inter-LAN connection and the bridge, respectively. For example, W-intra and W-inter denote the window sizes for intra-LAN and inter-l_AN connections, respectively. Figures 6a and 6b show the internetwork performance for the case of W-intra--W-inter, LT = 4ms, and AP = 25 ms. Figure 6a shows the average delays at MAC queues, transport queues and the internetwork link queue. Average end-to-end delays for intra-bAN and inter-LAN connections are also shown in the figure. The throughput per intra-LAN and inter-bAN connection are plotted in Figure 6b. These figures indicate that numerical results are in good agreement with the simulation results. From Figure 6a we see that for small window sizes, the system bottlenecks are in the transport layer (as well as in the internetwork link for inter-bAN connections). As the window sizes reach such values that the system throughput becomes saturated (this happens in Figure 6b for window size larger than 12), the bottleneck shifts to the MAC layer. The influence of the message generation time AP on throughput is presented in Figure 7, where we compare the throughput for the cases of AP = 25, 50 and 100 ms. We note that by keeping W-intra = W-inter, the throughput per inter-LAN connection can never exceed the throughput per intra-bAN connection. Next, we demonstrate the effect of changing the window size W-inter. The average delays and throughput for the case with AP -- 50, LT = 6 ms, W-intra = 8 and Winter = 1,2 . . . . . 40 are shown in Figures8a and 8b, respectively. In this case, except for very small values of W-inter, the internetwork link is the bottleneck. This is true in almost all practical systems where the internetwork link capacity is smaller than the transmission capacity of the bANs. We observe that when W-intra is fixed, the throughput per inter-LAN connection can be varied by changing the window size W-inter, and it is possible for inter-bAN throughput to exceed the intra-LAN throughput (per connection), even with the internetwork link as the bottleneck. However, this situation will change when the transmission capacity of the internetwork link is reduced to a certain level, as shown in Figure 9, which gives the
109
performance analysis 200
0.12
Inter-LAN I00 0.10
Intro- LAN
%) End-to-end
0.08
Transport
8,
- inter
Transport - intra
=o
P
o.o6
Per intro-LAN connection
.E F-
IO
Per inter- LAN connection
0.04 MAC-b MAC -intro
Internetwork
link
0.02
MAC -inter
I.O " I 0 a
I
I
I
I IO
I
I
I
I
o 20
W - i n t r o , W - inter
I o
b
I
I
I
I I I0 w-intro, W-inter
I
I
I 20
Figure 6. (a) Average delays in the case with W-intra = W-inter, AP = 25 ms, LT = 4 ms; (b) Throughput in the case with W-intra = W-inter, AP = 25 ms, LT = 4 ms
o.12
0.i0-
i --.- . . . . /
16
/
/
/
/
0 08 -
J
/
/I
~
/
/
/
Z
:--
.,~.
/
system performance for the case with LT = 12 Ms, and with other system parameters the same as in Figure 8. In Figure 9, due to the increased link processing time, the inter-LAN throughput per connection is always less than the intra-LAN throughput per connection, no matter what values W-inter may take. The impact of the bridge processing time to the internetwork performance is similar to that of the internetwork link transmission capacity. Therefore, the corresponding curves are not included in this paper.
i 0.06 -
//
I-
CONCLUSION
AP:25 /
C' / o.o
-
o.o
_
/ /;P:50
,I///
/
. yAP=
I00
I
I
'/,/.y o
I
0
I
I
I
I0
I
I
20
W- intra, W- inter
Figure 7. Throughput comparison W-intra = W-inter, LT = 4 ms
1I 0
in the cases with
In this paper we have investigated the end-to-end performance of interconnected token-ring LAwNs. The end-to-end intra-LAN connections are modelled as a single-chain closed queueing network, while the end-toend inter-LAN connections are modelled as a multiplechain closed queueing network. The performance model of the system was solved by an iteration algorithm with the aid of the MVA method. Numerical examples and computer simulations were presented to show the performance characteristics of the interconnected system. Our results indicated that the transport layer window size, the bridge processing speed and the internet link speed have significant influences on the end-to-end inter-l_AN performance.
computer communications
performance analysis 0. I0 I000
inter- LAN
Intro-LAN
~__._._...~~
0.08
I00
0.06
I0 ~
~i
MAC-b
0
I I0
oo21
Transport -intro •
I 20 W-inter
a
Per intro- LAN connection
~- 0.04 nsport- inter
inter t
l
k link
MAC-intro I 30
I I0
0
40
b
] 20 W-inter
I 30
40
Figure 8. (a) Average delays in the case with AP = 50 ms, LT = 6 ms W-intra = 8, W-inter = 1,2. . . . . 40; (b) Throughput in the case with AP = 50 ms, LT = 6 ms W-intra = 8, W-inter = 1,2 . . . . . 40 0.10 Inter- LAN
IOOC
0 08
Per inter- LAN connection 0.06
I00
£ .c ~- 0 0 4
e
//•
MAC
002
Tronsport- inter
0
oo
I0
a
20
30
0
40
w-inter
Per intra- I_AN connection
1 tO
b
[ 20 W- inter
I 30
40
Figure 9. (a) Average delays in the case with AP = 50 ms, LT = 12 ms W-intra = 8, W-inter = 1,2 . . . . . 40; (b) Throughput in the case with AP = 50 ms, LT = 12 ms W-intra = 8, W-inter = 1,2. . . . . 40
There are some problems with such interconnected systems which need further investigation: I System performance in asymmetrical cases, e.g. the two token-rin~ have different configurations and characteristics. 2 System performance when the bridge has a higher priority than user stations. 3 System performance with server/client configuration (as in Murata and Takagi6).
ACKNOWLEDGEMENTS
REFERENCES 1 Kummerle, K, Limb, J O and Tabagi, F A (eds) Advances in Local Area Networks IEEEPress, NY, USA
(1987) 2 Exley, G M and Merakos, L F 'Throughput-delay performance of interconnected CSMA local area networks' IEEE J. Selected Areas in C o m m u n . Vol 5 No 9 (December 1987) pp 1380-1389 3 Tanenbaum, A S C o m p u t e r Networks (2nd edn) Prentice-Hall, NJ, USA (1988) 4 Hawe, B, Kirby, A and Stewart, B 'Transparent interconnection of local networks with bridges' in
Kummerle K, Limb, l O and Tabagi, F A (eds) The authors would like to thank the anonymous referees for their comments and suggestions on this paper.
vol 14 no 2 march 1991
Advances in Local Area Networks I EEE Press, NY, USA
(1987) pp 482-495
111
performance analysis 5 Heath, J R 'Analysis of gateway congestion in interconnected high-speed local networks' IEEE Trans. Commun. Vol36 No8 (August 1988) pp 986-989 6 Murata, M and Takagi, H 'Two-layer modelling for local area networks' IEEE Trans. Commun. Vol 36 No 9 (September 1988) pp 1022-1033 7 ANSI/IEEEStandard 802.5, Token RingAccess Method IEEE Press, NY, USA (1985) 8 Kuehn, P J 'Multiqueue system with non-exhaustive cyclic service' Bell 5ysL Tech. J. Vol 58 (1979) pp 671-698 9 Boxma, O J and Meister, B 'Waiting time approximations for cyclic-service systems with switchover times' Perf. Eval. Vol 7 (November 1987) pp 299-308
112
10 Zahorjan, J, Eager, D L and Sweillam, H M 'Accuracy, speed and convergence of approximate mean value analysis' Perf. EvaL (1988) pp 255-270 11 Reiser, M 'A queueing network analysis of computer communication networks with window flow control' IEEE Trans. Commun. Vol 27 (August 1979) pp 1199-1209 12 Meister, B W, Janson, P A and Svobodova, L 'Connection-oriented versus connectionless protocols: a performance study' IEEE Trans. Comput. Vol 34 (December 1985) pp 1164-1173 13 Sauer, C H, MacNair, S A and Kurose, l F The Research Queueing Package Version 2; Introduction and Examples IBM TJ Watson Research Center, NY, USA (April 1982)
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