Modelling end-to-end protocols over interconnected heterogeneous networks

protocols

Modelling end-to-end protocols over interconnected

heterogeneous networks A Wolisz and R Popescu-Zeletin investigate the performance of end-to-end communication in interconnected heterogeneous networks

The performance aspects of end-to-end communication in interconnected heterogeneous networks are investigated. The individual networks to be connected (e.g. LANs, hi~hspeed LANs, X.25 networks, WANs including satellite links, ISDN, B-ISDN) differ significantly in their quality of service. On the other hand, requirements imposed by applications also differ significantly. Thus there is no single protocol stack which is optimum for all cases, and decisions have to be made on a special case-by-case basis. Motivated by the planned European space mission, for which a proper protocol stack assuring reliable end-to-end communication between application processes residing in space labs and ground-based appfication processes has to be chosen, a novel, top down modelling approach is developed. Rather than combining models of individual subnetworks, we represent any type of subnetwork by a specific set of network quality of service characteristics, and model the transport protocol so as to express the obtainable transport quality of service. Using such an approach it is possible to decide what kind of technological constraints have to be imposed on the parameters of a subnetwork A, which is to be connected to the given subnetworks B and C so as to assure the desired end-to-end quality of service. Keywords: networks, interconnection, protocols, modelling

With the massive deployment of solutions, differing essentially in technology and offering different qualities of GMD-FOKUS. TU-B, Hardenbergplz 2. l)-1000 Berlin 12. Cerrnany Paper received: 29 October 19qt;: revised paper re( eived: ~Mart h 1991

service, interconnecting heterogeneous networks becomes an important topic. According to the characteristic of the networks being interconnected, and the required quality of end-to-end transmission, different protocol stacks can be applied. One, already classic, controversy refers to the choice between link-by-link and edge-to-edge error control. Thus, depending on the networks to be interconnected, it is possible to use a connectionless transport protocol over a high quality network service offered by individual subnetworks, or alternatively, a connection-oriented transport protocol on top of a low-quality network service. Both possibilities have their strong supporters (e.g. Burg et al. 1 versus Piscitello et al.2), giving arguments of different type and significance. It cannot be expected that one of these solutions could generally succeed; rather, experience proves that decisions have to be made for individual cases. First attempts to develop a proper model are due to Ireland and Pujolle 3. Several significant contributions followed 4-~. Common to all these papers, however is an approach which consists of first defining some models for the individual subsystems, and later combining them to obtain the end-to-end characteristics. Alas, the conclusions reported in those papers differ significantly. This is a consequence of the different assumptions about the characteristic of individual subnetworks, and also due in part to differences in the functionality of the transport protocol modelled. Rather than discussing the assumptions made in each of these papers here, this paper outlines how the proposed solution encompasses the earlier work. In this paper we develop a different approach referred

0140-3664/92/001011-12 © 1992 Butten~vorth- Heinemann Ltd vol 15 no 1 january/february 1992

11

protocols to later as the top-down approach. Rather than combining models of individual subnetworks, we represent any type of subnetwork by a specific suggested set of network quality of service characteristics, and model the transport protocol so as to express the obtainable transport quality of service via these characteristics. Certainly, given a model for each subnetwork it is possible to compute the proper characteristics, and eventually obtain the transport quality of service parameters. However, with this approach it is also possible to decide, for example, what kind of constraints have to be imposed on the parameters of a subnetwork A, which is to connect with given subnetworks B and C so as to assure the desired end-to-end quality of service. The remainder of this paper is structured as follows: first we review an example of heterogeneous internetworking--communication for the European space mission -- followed by a brief summary of the two major alternatives for intemetworking. We then introduce the main concepts of our top-down approach, focusing on the assumptions about individual subnetwork characteristics, as well as on features of the transport protocol which have been included in the analysis. Based on the proposed methodology, an approximate queueing analysis of the transport protocol is developed. Finally, for the subnetworks to be interconnected, we validate the approach using simulation. Conclusions about the model developed and the results derived from the case study upon which we focused conclude the paper.

COMMUNICATION MISSION

IN T H E E U R O P E A N SPACE

Europe plans a permanent space mission including several advanced projects in a wide range of fields such as manned spaceflight, rendezvous and docking, retrieval of satellites and remote-controlled robotics (telescience). All these projects, which will be carried out in several missions, require reliable data communications between low earth orbiting (LEO) spacecrafts (approximately 600 km) and the ground. The topology proposed by the European Space Agency (ESA) is a Data Relay System (DRS), with two satellites in geostationary earth orbits that can each provide two-way communication links between LEO spacecrafts for 80% of their orbits and earth terminals located in Europe (see Figure 1). Data is uplinked from an earth terminal to one of the DRS satellites, which relays it to a LEO spacecraft, and vice versa. In a small region of its orbit the LEO-spacecraft cannot communicate with the DRS; this region is called the zone of exclusion, or the noncoverage zone of the global system. A LEO spacecraft will communicate with a European earth terminal via one DRS satellite for part of its orbit and with the other DRS satellite for the remainder. As a result of the above considerations, physical connectivity between space and ground will be missing across the zone of exclusion, and during a short period of time during which the LEO spacecraft transfers the satellite link from one DRS satellite to the other. For a

12

Geostationary

".

""

.

.

'-.

Control centre

Wide Area

Network

LANs

LANs

Figure 1. European Space Agency's proposed communications topology

detailed description of the global architecture and the technical solutions for maintaining the logical connectivity over the exclusion zone and link transfer, the reader is encouraged to refer to Lenzini and Popescu-Zeletin 7. The earth-terminals relay data from the end-systems situated all over Europe to the DRS/LEO spacecraft, and vice versa, via wide area networks (WAN). The overall system, referred to below as a global system, comprises three interconnected subsystems through which data is conveyed between an experiment in the LEO spacecraft and the ground end-systems:

1. Spacecraft subsystem: provides end-systems interconnection within a spacecraft. Due to the data volume required, FDDI technology will be used in the spacecraft. 2. Satellite subsystem: provides the communication pipes through which data can be transferred between a spacecraft and its supporting ground terminals. 3. Ground subsystem: provides communication between earth terminals and ground end-systems. It includes a variety of private and public ground subnetworks (varying from LAN to ISDN). While the communications architecture for endsystems attached to the spacecraft and ground subsystems conforms to the ISO's Open Systems Inter-

computer communications

protocols protocol in the transport level over connectionless network services in the different networks interconnected. The questions to be answered are:

connection Reference Model (OSI/RM), the communications architectures for systems attached to the satellite subsystem comply with the Advance Orbiting System Architectures (AOS), designed by the Consultative Committee for Space Data Systems (CCSDS). The global system which results from the interconnection of the three subsystems (by means of gateways) should support, in an integrated way, different applications with different traffic characteristics. The reference internetworking configuration is shown in Figure 2. This configuration consists of the AOS system which is interconnected within the LEO spacecraft to a token bus or FDDI by means of a gateway (L-IWU), and on the ground to a connection-oriented WAN via another gateway (G-IWU). The internal structure of the ground subsystem can involve a number of interconnected local and wide area networks.

1. Given a certain set of requirements for end-to-end communication, which parameters must be met in the implementation of each interconnected subsystem? 2. Given a specific technology set (type of network, protocol stacks) for two subsystems, which technology should be chosen for the third subsystem from a number of alternatives? In our case, AOS in subsystem 2 and token bus in subsystem 1, what should be the characteristics of subsystem 3 (X.25 or ISDN) to meet end-to-end requirements? 3. Based on the characteristics of a subsystem (error probability, arrival rate control, etc.) at the lower layers in different network types, how do the protocol profiles (connectionless or connection-oriented) influence the performance of that subsystem? In the next section we introduce the top-down methodology to help the decision process in the design phase of a global system where only the end-to-end requirements are defined, and where the system designer is faced with design choices in different network technologies, different hardware/software supports for the gateways, and different protocol stacks.

INTERNETWORKING ARCHITECTURE In interconnecting subsystems, two sets of problems have to be faced while designing the global network service provider. One set deals with the services provided by the sybsystems to be interconnected, which are of a different type and quality. The other set is the service-type visibility of the global network users. Two strategies can then be identified to perform subsystems interconnection, which may be distinguished according to the type of service used to perform interconnection: connection-oriented (alternative A) or connectionless (alternative B)8'q. The choice in the ESA architecture is to adopt the ISO class 4

TOP-DOWN MODELLING A S S U M P T I O N S The aim of top-down modelling is not to model a certain choice of elements, but rather to give answers for each subsystem in the global system which has to meet certain DRS

ES

L/|WU

Subsystem 1 Figure 2.

G/IWU

Subsystem2

rld~~ two~_~

ES

Subsystem3

Int erc onnection scenario

vol 15 no 1 january/february 1992

13

protocols Endsystem

Endsystem End-to-endClass4 protocol

Level3 •

•

o

.

.

.

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.

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M,

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Figure 3. View of interconnected networks used for the top-down approach. E: endsystem; G: gateway; ~-i: stream of arriving packets; qi: probability of packet rejection (overflow); Pi: probability of bad transmission; Mi: number of buffers; Ki: capacity of the servers predefined requirements. Hence, we model only the entities involved in end-to-end communication, aggregating the underlying levels in theses entities (Figure 3). The model consists of two end-systems interconnected through a number of different subnetworks, each pair of subnetworks being connected via a gateway. In our approach we identify within the end-systems and gateways only the transport and network entities. We explicitly consider the transport layer protocol, and focus on an analysis of the data transmission phase, ignoring the connection establishment/termination phase. The operation of the transport layer results in the production of TPDUs (transport protocol data units). For this study we assume a 1:1 relationship between TPDUs and network service data units (NSDU). NSDUs will be transmitted via different networks and routed in the gateway by the network entities towards their destinations. Any network protocol could be used. The key assumption for our approach is to neglect the details of the network protocol, the underlying network technology, network access protocols, etc. What really matters for this method is the network service, described in terms of offered characteristics. The network service is modelled as a pair of cooperating network entities in each subnetwork, as presented in Figure 3. We assume that this service will be described by some queueing network of total internal capacity K,.

14

demands, in front of which a queue of capacity limited to Mj demands may form. Demands (NSDUs) arrive with a rate hi in each subsystem in the interconnection chain. We do not introduce any specific assumptions about the structure of the queueing network; we only assume the availability of some characteristics describing the quality of service given by such a subsystem. The following characteristics will generally be needed: 1. qi = Qi(2i) (1) defining the probability of an arriving NSDU being rejected because the input queue is full. This probability depends, in general, on the arrival rate. This represents all capacity constraints within a subnetwork and a gateway, including flow control within a subnetwork and buffer assignment within the gateway. 2. Pi, defining the probability of an NSDU, which has been accepted into the queue, being lost within the network of queues, e.g. within the network layer (e.g., because of errors which are not recoverable within the network layer). We assume below that Pi is a constant. Allowing for the dependency of Pi upon 2i is an easy extension. 3. wi = WiO.i) (2) defining the mean delay within the i th subsystem for demands which have neither been rejected or lost. This delay is understood as the sum of possible

computer commumcations

protocols waiting time in the input queue and the processing time within the queueing network, and is dependent on A i. 4. Additionally, for each subsystem, we introduce: hi, vi (3) defining the mean value and the second moment of a TPDU's processing time, which is understood as the interdeparture time from the input queue (these are two moments in the time between acceptance of two consecutive demands = NPDUs from the input queue, under the assumption that the input queue is not empty). In fact, we use only b0 and v0 in the analysis. These values, generally, depend both on Aj and on the number of demands actually within the subsystem. For simplicity we neglect these possible dependencies. Let us stress that the detailed form of these characteristics is unimportant for our general methodology. What really matters is the ability to obtain proper values of qi and wi for any given )-i. Thus these values could, for example, be obtained from simulation runs performed individually for each ~ , or they could be read from curves plotted as a result of some eadier, independently performed experiments. Let us recall that such representation of the network service is general, covering all possible connectionless or connection-oriented protocols. We model the operation of the transport entities themselves in an identical way, along with the interoperation between the adjacent transport and network entities within each end system (assuming, however, an unlimited queue size). This reflects the assumption that data units are not lost within a single end system. Thus, to model a configuration consisting of two end systems connected via some subnetworks we use (L + 1) subsystems, denoted So, $I . . . . . SL. Subsystems So and St represent processing within the transport entities, as well as the connections between adjacent entities in endsystems, while subsystem S~. . . . . St i represents the individual subnetworks. We assume that the first subsystem is offered a Poisson stream of demands with intensity A, to be transmitted. The adopted transport protocol is the ISO/OSI Class 4 protocol m. We concentrate first on the error recovery, neglecting at this time the end-to-end flow control specified in ISO 8073 l°. It could be also interpreted as assuming that the window will always be large enough to not prevent the sending of TPDUs. Following ISO 8073 m we assume for the error control that: I. After transmitting each TPDU = NSDU, a timeout (Timer TI in the Class 4 protocol) with value T is started. Each transmitted TPDU is buffered in case retransmission should be necessary. 2. EachTPDU is numbered, and has to be acknowledged by the receiver. This may occur either via an explicit ACK-TPDU, or via piggy-backing with another TPDU travelling through the system in the opposite direction. 3. If the acknowledgement of some TPDU, say with number X, is not obtained prior to timeout activation, the sending party stops transmitting additional TPDUs,

vol 15 no I january/february 1992

retransmits the TPDU number X, and all other TPDUs which were transmitted later (i.e. between the previous transmission of the TPDU number X and its retransmission (the Go-Back-N strategy). 4. The receiver is obliged to acknowledge the TPDUs obtained in proper sequence, and drop TPDUs obtained out of sequence, which will be retransmitted anyway. This is not the only possibility allowed by ISO 8073 I°. As correctly pointed out by Svobodova et a l l I nothing is said explicitly about the retransmission strategy in [ISO 8073]. The receiver could store the TPDUs obtained out of sequence and use them later for resequencing. On the other hand, the transmitter can retransmit, upon expiration of timeout, only a single TPDU. Notice, however, that this does not mean it is possible to retransmit only TDPDUs in error. As pointed out by Collela et al. ~, before the retransmitted TPDU will be acknowledged, the timeouts for several following TPDUs expire. It can easily be seen that given ideally set timeout values, all the TPDUs sent after the TPDU in error will be retransmitted! From the delay point of view, it is definitely better to retransmit these TPDUs immediately, not one by one. As a matter of fact, the same argument also applies to the TCP protocol. Thus the equivalence ISO Class 4 protocol -- Go-Back-N strategy is commonly accepted.

APPROXIMATE SOLUTION We present an approximate solution for the model introduced. From the performance point of view, we are primarily interested in obtaining the throughput-delay characteristics. Let us note that any TPDU can be retransmitted several times before it will, eventually, be successfully delivered to the receiver. According to equation (2), the delays depend on the arrival rates offered to the individual subsystems. Thus we have to determine the arrival rates of customers and the probability of retransmission. We assume that all arrival rates are Poisson. As illustrated in Figure 4 with dotted recirculation lines, in addition to the originally offered load A, the first subsystem has to carry a retransmission load A~; ~.o =

A +

AR

Several reasons contribute to this retransmission load: 1. NDSUs may be lost due to overloading (blocking) of the subsystem Si with probability qi, or due to transmission problems within the subsystem Si with probability Pi. Thus the customer arrival rate, as offered to consecutive subsystems, decreases, and finally At is offered to the last subsystem. 2. A TPDU is retransmitted as seemingly lost if it has successfully made its way to the receiver but an acknowledgement has not been properly received by the sender, due either to timer expiration before the acknowledgement arrived, or to loss of the acknowledgement. The probability of such retransmission

15

protocols

Ag±_,. r 2~o

Ii-I I I I

I I I I

~mI

I I I I

I I I I

Xl PF

AR

•i

.........

::i

',: -"

...:

:::::::::::::::::::::::::::::::::::::

::!

!::::::!iii!ifi

:::::::::::::::::::::::::::::::::::::::

i:;::::

::::::::::::::::::::::::::::::::::::::::

......

:::

I

1::::::::::::"

L_t

i i i i i i i i NetwOrklayer : ~ i i i i i i i i i i i i i i i i i i i ~ i i i i i i i i i i i i i i i i i i i i i Figure 4.

Schematic representation of the data unit flow

is equal to PT. With this probability, the receiving transport entity will find one TPDU in the arriving TPDUs (which has been retransmitted as seemingly lost), recognize it as a duplicated TPDU, and drop it. 3. Due to the Go-Back-N retransmission strategy, several TPDUs following a lost or seemingly lost TPDU are dropped by the receiver, and retransmitted by the sender. The probability of finding such an out of sequence TPDU is denoted by P~. As a result, the arrival rate of received packets is reduced to ~-z. What makes computation of the arrival rate ~0, and all other arrival rates hi, difficult is the fact that the probabilities qi, i = 1, 2 . . . . . L - 1, P~ and Pr depend on the arrival rates offered to the individual subsystems. An iterative schema for computing the arrival rates has to be developed. This scheme - - presented in Figure 5 - - can be summarized as follows: Let us note that the output rate from the whole system is definitely equal to the global input rate A. Assuming some initial values PF0 and Pro for the probabilities PF and PT, respectively, we may observe that:

Solving for Zi under the assumption and PT are known

that PF

Let us consider some arbitrary subsystem Si, i = 0, 1 . . . . . L. The conservation law lets us state that: 2~i = ,,1.i + ~/[(1 - pi)(1 - qi)]

(5)

where we assume P0 = qo = PL = qL = O. On the other hand, equation (1) relates the value qi to )'i for j = 1, 2 . . . . . L - 1. Thus, if only the value of ~-i+ 1 were known, then the system of equations (1) and (5) could be solved for the two unknown values h i, qi" Numerical solution, however, seems necessary for the general case. As the value of ~-t + 1 is given by equation (4), working backwards subsystem by subsystem, this means that by solving consecutively for j = L - 1, L - 2 . . . . . 0 the system of equations (1) and (5), we obtain a first approximation for all the values '&i and qi, i = L - 1, L - 2 . . . . . 0.

Solving for PF ),, = A/(1 - PT)

t

(4)

)-t + 1 = ~-7/( 1 - PF) ) Additionally, the procedure can be divided into three steps: • solving for ~ under the assumption that PF and PT are known; • solving for PF, the probability of TPDU being dropped; • solving for PT, the probability of TPDU being seemingly lost.

16

Having the approximation for the ~.i, qi; i = o, 1 . . . . . L it is possible to start computing a better approximation P~ for the probability of packets being dropped. Let us first compute PLOSS,the probability of a packet being lost during transmission. It easy to see that: L-1

i

1

PLOSS = > i F, H ( 1 i=1 i =1

- Fj)

(6)

i

computer communications

protocols As discussed earlier, both the lost and seemingly lost TPDUs cause retransmission and dropping of the out of sequence or repeated TPDUs. Notice that not all lost or seemingly lost TDPUs have such an effect; among them could also be some TPDUs which would themselves be dropped. In fact the probability Pit that a TPDU will be lost and cause some dropping (we shall call such a TPDU a leading one) can be defined as:

4

Ptl = (1 - P~). P[oss

I XL*I =;',Z/(1 --PF)

Thus the probability P[ of a TPDU being dropped is given by:

i=L_ 1

_1

_,-7]

(9)

P~ = Ao" T'Pll

(10)

as the number of TPDUs being dropped after the leading one is equal to Ao'T. Substituting equation (9) into equation (10), and solving for Ptt, we obtain:

Computing Xi, qj according to (1), (5)

Pll = P~OSS/(1 + A0" T. P~-OSS)

(11)

and finally: P; = A 0 • T- P[oss/(1 + ~0" T. P[oss) Computing P~I according to (6)-(12) X = PF

-

PF =PF - Q ' X

After applying formulas (6)-(12) we always obtain a new approximation P~ of the probability of the packet being dropped, using the PF approximation to compute the values of Ai. Let us denote by X the difference:

]

]

P;:

I

PT = P T - Q " Y I

I x/PF I < z~

(14)

(5 a constant > 0, [I denotes absolute value) we consider this step as finished, and use the obtained P~ as a valid approximation of the dropping probability in the next step. If equation (14) will not be satisfied, we assume:

Figure 5. Methodology for computing data unit flows where: for j = 1,2 . . . . . L - 1 f o r j = 0, L

(7)

On the other hand, the joint probability of a packet being lost or seemingly lost is equal to: L-1

PT" I-I (1 - Fi) I=1

vol 15 no 1 january/february 1992

where

0
(15)

and repeat both Steps 1 and 2 for this new value. Let us note that by using the initial value PF0 equal to 0 we would obtain the results of the first iteration arrival rates as well as Ptoss for the case of the selective reject error correction schema (only the TPDUs really lost are retransmitted).

NO

P[oss = Ptoss +

(13)

PF= Pr-aX,

I

t Fi=qi + p i - q i ' p i Fi=O

X : P~ - P; If:

NO

I Computing P~accord ng to (16)-(27

(12)

(8)

Determining the end-to-end delay Before starting the final step of our iteration, let us consider the end-to-end delay experienced by a TPDU, assuming - - as previously -- the complete knowledge of all the arrival rates. To do this let us observe a TPDU which has arrived at the queue in front of subsystem So. If no retransmissions were necessary, then this TPDU would experience a total delay: I D* = ~ wi ;:0

(16)

17

protocols being the sum of delays experienced in individual subsystems. Individual values wi are given for each subsystem Si by formula (3), with the properly substituted value 2i. With the probability PFR it may occur that our target TPDU follows a TPDU which has been lost (a leading TPDU), and thus a retransmission will be necessary. Let us stress that PF~ reflects only the case when a leading TPDU has been lost; contrary to PF it does not include the case when a leading TPDU was seemingly lost!! Obviously, retransmissions due to seemingly lost TPDUs influence the load, but do not influence explicitly the end-to-end delay of the TPDUs involved, as in fact those TPDUs arrive at the receiver and are processed there. The probability Ptt~ of a leading TPDU being lost (and not seemingly lost), and the probability P~ of a TPDU being invalid as a result of previous loss, can be determined in a similar manner to formulas (9)-(12), substituting only P[oss by PLOSS.Thus:

PFR g/(1 + g) =

where

g = ~-o'T'PLoss

PLLR = (1 -- P~R)"Ptoss

(17) (18)

During its retransmission, the target TPDU could also follow some TPDU which has been lost, and the situation may repeat several times with equal probability PFR.It can easily be shown that the mean number of such retransmissions is given by No: No = PFR/(1 - PFR)

(19)

as. the probability of exactly i retransmissions is equal to P~R"(1 - PFR). In the case of the first retransmission we can assume that, on average, a time period equal to 2. 1-/3 will pass between the completion of the processing of the target TPDU within the subsystem So and the action of a timeout due to the loss of some leading TPDU. This can easily be computed under the assumption that both the leading TPDU and the target TPDU are equally probable to be any of the transmitted TPDUs. However, before a retransmission can start, the processing of a TPDU actually being processed (if any) should be completed. This action takes a time with a mean value well known from basic queueing theory: W m = V0/(2. b 0)

(20)

while the probability of any TPDU being processed is equal to 20 * b0. Afterwards, retransmission of the TPDUs starts. As explained earlier, on average (,,!.0*T) TPDUs will be retransmitted, each one needing, on average, the processing of length b0. As our target TPDU will be, on average, in the middle of the retransmitted group (preceded by ~0 T - 1)/2 other TPDUs), the time spent until its retransmission is completed could be approximated as WRET: WRE T = [ 0 ° 5 ( 2 0 • T -

1 ) + 2]b 0

(21)

This is a delay which out target TPDU would experience in

18

the absence of further retransmissions. Let us now consider the case of several consecutive retransmissions. As both the leading TPDU and the target TPDU are equally probable to be any of the retransmitted TPDUs, the target TPDU will, on average, follow the leading TPDU by20- T/ 3 customers. Thus the time between two consecutive timer actions due to the loss of a leading TPDU will, on average, be equal to IT + 20- T- b0/3]. Additional delays for the following retransmissions are identical to that of the first one. If, finally, our target TPDU does not follow any lost TPDU, we have to consider the possibility that it will itself be lost, which may happen with probability PttR, as given by equation (20). Loss of this target TPDU may happen several times, with an equal probability. The mean value of retransmissions, is equal to NI: (22)

N1 = PLLR/( 1 -- PLLR)

Each time the target TPDU is lost, it suffers an additional delay equal to (T + 20. b0" W m + bo), being the sum of timeout value, the time needed to complete the processing of a TPDU being processed, while the timeout is activated (if any), and the processing of the target TPDU itself. Considering all the cases described so far with proper probabilities, we finally obtain the end-to-end delay

D(A): L

D(A) = ~

WiOti) + [2. T/3 + WREv -- T×]. PFR

i=0

+ No" [T× + 2o" bo" WiN] + Nl"[T + )to'bo'Wm + bo] where T× =

(23)

+ bo'Ro" T/3.

Solving for PT In the last step we solve a better approximation P~ of the probability of TPDUs seemingly lost. In the literature it is mostly assumed that acknowledgements do not experience losses, nor do they influence the load of the links (e.g. they use a separate ideal link). In addition, it is usually assumed that the timeout value is set properly, meaning that timeouts cause retransmission only if it is really needed. If this approach is followed, no seemingly lost packets would exist. Thus the initial value Pro could be simply chosen as O, and one could immediately start computing the desired delay characteristics, using the results obtained so far. Following the assumptions introduced above, we consider cases where: • acknowledgements experience a delay on their way back similar to that of the TPDUs which were originally transmitted; • acknowledgements may be lost on theirway back with an identical probability as the original TPDUs;

computer communications

protocols • acknowledgements may arrive late, e.g. after the timeout for a proper TPDU has already acted.

M,

r

1 Xi+I

Reflecting these assumptions we can compute P~ as: P~ = PLOSS+ (1 -- PLOSS)"Pu

(24)

qi

I

where: PLr = 1 - Z(T)

(25)

Z(x) being a distribution function of the time needed to receive an acknowledgement after the timer has been set, under the condition that an acknowledgement will be received at all (acknowledgement round-trip delay). The main problem there is that we do not exactly know how the acknowledgement round-trip delay is distributed. Therefore, we decided to approximate the distribution of this delay with a k th order Erlang distribution, having the probability density function:

pkOakt)l,-1 fa(t) =

,,~t

(k - 1)!

e

1

p

Var[t] =

1 1

p2 k

(27)

Figure 6.

Pl

DEFINITION

EXAMPLE

The approximate analysis presented above allowed quite general assumptions concerning individual subsystems. To present some quantitative examples, we further constrain ourselves to a specific type of subsystem. We have chosen the same case as used by Barghava et al. 6, which is considered as proper for many realistic cases. We assume that each subsystem consists of an exponential server characterized by service intensity Pi, followed by an infinite server with constant service time ri (cf. Figure 6). This represents the processing of each TPDU followed by some transmission delay. We assume a limited queue length M, in front of subsystems S~, $2 . . . . . 51 I, while M~j = M 1 = ~c. Let us denotep, = ,~.,/,ui, i = 0, 1 . . . . . L; Gi = ~i(1 - qi); i -- 1,2 . . . . . L. Using the well known queueing formulae, we obtain for this case specific forms of formulae (1), (2) and (3) which are denoted by (la), (2a), (2b) and (3a): (I - pi)p~' I -~, i ~ fl

we consider this step as finished, and use the obtained P~as a valid approximation for the probability of TPDUs being seemingly lost. If formula (29) is not satisfied, we assume:

fori=

1

w, =

if p~ = 1

I 1 { Pi Gi -1 Pi

Pi 1 .... + r, 1 - P i Z,

hi = 1/,u,;

(la)

if p = 1

f o r i = 1,2 . . . . . L - 1 w, =

1,2 . . . . . L - I

(Mi+ 1)p(Mi+ 1) I 1 p(Mi+-l) ) + ri ifpiV= 1

0.5"Mi/G + ri

0
and repeat the procedure (Steps 1-3) for this new value. Let us note that using the initial value P7 equal to 0, we obtain as the result of a first iteration characteristic for the case where no acknowledgements are lost, and the timeout acts only if needed. This intermediate result may be interesting for the sake of comparison. Using, additionally, PF = 0, deleting equations (8)-(15) and replacing (17) by Pr~ = 0, we obtain a complete analysis of the selective reject case without the assumptions of perfect timout and no lost acknowledgements.

if p, =~ I

Mi + 1

(29)

vol 15 no I january/february 1992

~ki+l

Example subsystem definition

qi=

If:

PT=PT-a.Y,

-V

0 ,r i

(28)

I¥1PTI < 8

0

qi

SUBSYSTEM

The common feeling is that the mean value should be exactly equal to the doubled delay D* as defined by equation (16). We were unable to find any suggestions for the variance. Note that by varying the order of distribution k we may change the variance significantly. Increasing k means approaching the deterministic case. After applying formulae (24)-(27) we always obtain a new approximation P} of the probability of the packet being seemingly lost, using the old approximation to compute all values in the previous steps, and the mean end-to-end delay. Let us denote by Y the difference: Y= PT-P;

M,

(26)

with the mean value and variance given by: E(t) =

p,

v; = 2/pf

for i = 0, L

(2a) (2b) (3a)

Numerical results reported below have been obtained for the case of three interconnected subnetworks (L = 4). In order to investigate the size of the approximation error, we have compared the mean delays obtained from our analysis with the results of digital simulation. Due to the inherent features of the investigated system the

19

protocols /

60

s

/ 50

b0 = b l =b4 = 1;

2"" • Y

40 s J

/

~'0 = T1 = T4 = 0; f f J"

.oi I ~.0 "s

30 I

0.2

l

0.4 0.3 Arrival rate

I

0.5

Figure 7. C o m p a r i s o n of results o b t a i n e d from the a p p r o x i m a t e s o l u t i o n (lines) with s i m u l a t i o n (points). System parameters: bi = 1.0; i = O, 1, 2, 3, 4; P7 = P2 = 10"* - 5;p3 = 10" - 3 ; M j = 6 0 ; r i = 5.0;j = 1 , 2 , 3 ; . . . . : T = 200; - - - - - : T = 150;--:T= 100

packet delay has a high variance, increasing rapidly for bigger values of timer settings, thus the confidence intervals obtained from simulation have also been fairly large. Several test runs executed for different sets of data confirmed, however, the general agreement of the analytical results with simulation (c.f. Figure 7). As for this example, the order of Erlang distribution, used for approximation of the acknowledgement round-trip-delay (c.f. formulae (25) and (28)) has been chosen with respect to the characteristics of individual subsystems as k = 50. The developed methodology is now used for the space mission design problem described above. The following parameters have been assumed: • The system is expected to offer end-to-end 25 kbits/s transport connections. The TPDUs used are assumed to be 1250 bytes long. • For subnetwork 1 (on-board token bus LAN) the service time of 10ms/TPDU (corresponding to a transmission speed of 1 Mbit/s) is assumed. The transmission delay is negligible. Bit error rate is 10 -7 , corresponding to the TPDU error rates i 0 -s. • For subnetwork 2 (satellite channel) the use of 500 kbits/s permanent virtual circuits is assumed. Thus the service time of subsystem $2 is equal to 29 ms/ TPDU follows. The transmission delay is assessed to be 290 ms, with a bit error rate 10 -12. • For subnetwork 3 (ground WAN) the use of 64 kbits/s links is assumed, which implies a service time of 170 ms/TPDU. Following the X25 network simulation results of Brady 12, a transmission delay of 10 ms has been assumed for this subsystem. • A service time of 10 ms/TPDU is assumed for the transport protocol implementations, and used as a parameter of subsystems SO and $4. The mean required end-to-end TPDU delay has to be smaller than 750 ms.

20

The time will be expressed in units of ten milliseconds. The transmitted stream of packets has the rate of 0.025/ time unit, and the parameters of the model considered are: b 2 = 2;

b~ = 17

r 2 = 29;

r~ = 1.

To demonstrate the described methodology we assume that the protocols and characteristics of subsystems 1 and 2 are already chosen, and we focus on the influence of subsystem 3 on the global system behaviour. In Figure 8 the mean end-to-end delay of the system has been depicted as a function of transport layer timer for different values of the bit error rate in subnetwork 3. The buffer capacity in all gateways has been chosen as 40 packets, which ensures a fully negligible ratio of TPDU loss due to the buffer overflow. The Erlang distribution of an order of 50 has been chosen for the acknowledgement round-trip delay. The desired mean end-to-end delay may be obtained in the case of TPDU error rate not exceeding 5.10 -3. The developed model reflects the system behaviour under different layer 4 timer settings. For increasing values of the timer setting, the mean end-to-end delay increases, and for small values of timer setting the mean end-to-end delay increases rapidly. It is the so called 'avalanche' effect observed in simulation studies described by Brady 12, but generally neglected in other analytical models of interconnected networks. This effect results from the rapid increase of the ratio of seemingly lost TPDUs with the decrease in timer setting. The difference between the layer 4 timer setting and the double end-toend delay is non-negligable. This difference clearly depends on the variability of the round trip delay of acknowledgements. In Figure 9 different values of the order K of the Erlang distribution modelling the acknowledgement round-trip delay have been assumed, in the case of a TPDU error rate of to 5.10-3. For an increased variability an increased layer 4 time is

./

/

90

/

80

D 70 60 I

I

I

I

;

I

I

200

250

300

350 T

400

450

500

Figure& M e a n e n d - t o - e n d delay D versus t i m e o u t setting T for different values of the TPDU error rate p~. (p.~ : 1 0 - 2; m : 5 • 1 0 - ~; . . . . : 1 0 - ~; - - : 5 • 1 O- 4; _ _ _ : I 0 -4

computer communications

protocols 95

flJ

90

85 D

i

80

90

/ f

85 80

75 w

L

70 J

75

t

200

300

400

500

T

Figure 9. Mean end-to-end delay

D versus

I

L

10

15

timeout

setting T for different values of the order k of Erlang distribution. P 3 = 5 " 1 0 - ~ . +: k = 8 0 ; X: k = 5 0 ; 0: k = 30; I1: k = 2 0 ; - - : k = 70; - - - - - - : selective reject; - - : ideal for back-N

required, but larger values of the timer setting lead to increased values of the mean end-to-end delay. The differences are quite large - - in the system under study for k = 80 the timer setting 1.8 s (180 units) is allowed, while for k = 10 the smallest timer setting is 2.6 s? It is important for the system calibration to estimate properly this variability - - or use 'pessimistic:' timer settings. Let us note, however, that in the system under study the desired mean end-to-end delay could not be achieved even for an error rate of 5 - 1 0 -3 if the 'pessimistic' timer setting exceeds approximately 2.7 s. In the next series of experiments we have considered the influence of limited buffer capacities. Due to the significant differences in processing time assumed for the individual subsystems, the requirements for the buffer space also differ for each subsystem. If the buffer capacities of subsystems 1 and 2 can be kept small, subsystem 3, being the bottleneck in the end-to-end communication, has to provide increased buffer spaces. Figure 10 outlines the influence of M~ on the mean endto-end delay, in the case of M I = M 2 = 5 for some values of the timer setting. In the case of a high TPDU error rate in subnetwork 13, the requirements specified for the end-to-end delay cannot be met. A possible solution for this case would be to reduce the error rate by applying some solutions local to this subnetwork (for example, one could use some additional error control). However, this would certainly lead to an increase in the mean delay experienced within the subnetwork. Originally, the mean time to pass subnetwork 3 (without regard to possible queueing in front of this subnetwork) has been equal to (b{ + ~{) = 18 time units. In accordance with our top-down approach, let us consider the following problem: assuming it is possible to decrease the TPDU error rate p3 to 10 -4, what increase in the mean time to pass subnetwork 3 is acceptable with regard to the end-to-end delay requirement?

vol 15 no 1 january/february 1992

I

5

[

20 M3

~

I

l

25

30

35

Figure 10. Mean e n d - t o - e n d delay D versus M~, the buffer capacity in front of subnetwork 3. - - - - - - : T = 366; m : T = 3 0 0 ; - - : T = 233

In Figure 11 we increase this value to b3 + (~3 + A) and plot the mean end-to-end delay versus timer setting for different values of A. Notice that values of A up to 90 ms can be tolerated. In addition, note that for this case the mean end-to-end delay is almost independent of the timer setting! This is the immediate consequence of the reduced TPDU error rate (compare to Figure 8). This makes it possible to ignore the acknowledgement round trip delay variability and use the 'pessimistic' timer setting without violating the requirements. The decrease in the TPDU error rate in subsystem 3 to 10 -4 , on behalf of increasing the mean time to pass the subnetwork up to 30%, is beneficial for overall performance. This would be an argument for the local error control within subnetwork 3. It is not necessary to consider in detail which error control method was used in enhancing subnetwork 3. Rather than analysing the possibilities available, the method outlines the required global parameters of this subsystem.

85 80 75

.~~ x

70 A

65200

250

300

Figure 11. Mean end-to-end delay D versus timeout setting for different values. A: increase in mean delay within subnetwork 3. TPDU error rate p~ = 10 -4 . X: A = 12; V : I I : /~ = 6; A : ~ = 3 ; 0 : A = 0

21

protocols CONCLUSIONS In this paper we have stressed the importance of a topdown approach. We believe that with the increasing complexity of interconnected systems, such an approach will prevail. Using the example of the European space mission we have demonstrated the possibility of imposing constraints on the TPDU error rate and delay within a single subsystem to satisfy end-to-end performance requirements. Which solutions should be adopted in designing the individual subsystem to meet these constraints remains a separate question. Using this approach we analysed which combination of individual subnetwork error/delay characteristics under the end-toend error control performance met predefined requirements. In developing the approximate solutions, very general assumptions about the characteristics of individual subsystems have been introduced, without requiring a complete analytical model of each subsystem. The approach presented makes it possible to model several protocol mechanism features used for end-to-end data transmission over interconnected heterogeneous networks. As for error control, we analysed the data unit error rates within individual subnetworks, loss of acknowledgments, use of timeouts for the recognition of data/acknowledgement loss, non-ideal timer setting and the Go-Back-N retransmission policy (the treatment of the selective reject case has been presented as a byproduct). In addition, we allow for finite capacities of intermediate buffers between interconnected subsystems. Studies of features mentioned above are reported in earlier papers; however, none of the solutions published so far have included all of these features in an integrated manner.

REFERENCES 1 Burg, F M, Chen, C T and Folts, H C 'Of local networks, protocols and the OSI reference model',

22

Data Commun. (November 1984) pp 129-150 2 Piscilello, D M et al. 'Intemetworking in an OSI environment', Data Commun. (May 1986) pp I 18-I 36 3 Ireland, M and Pujolle, G 'Comparison of two packet transmission techniques', IEEE Trans. Infor. Theory, Vol 26 No 1 (January 1980) pp 92-97 4 Kuhl, D 'Error recovery protocols: link-by-link vs edge-to-edge', Proc. INFOCOM 83, (1983) pp 319-324 5 Suda, T and Walanabe, N 'Evaluation of error recovery schemes for a high-speed packet switched network: link-by-link versus edge-to-edge schemes', Proc. INFOCOM 88 (1988) pp 0722-0731 6 Barghava, A, Kurose, J, Towsley, D and Vanleempul, G 'Performance comparison of error control schemes in high-speed computer communication networks', IEEE I. Selected Areas in Commun., Vol 6 No 9 (December 1988) pp 1565-I 575 7 l.enzini, L and Popescu-Zelelin, P 'From the Earth to the sky and back', IEEEJ. Selected Areas in Commun., Vol 8 No I (January 1990) pp 107-117 8 Burg, F and Di lorio, N 'Networking of networks: internetworking according to OSI' IEEE ]. Selected Areas in Commun., Vol 7 No 7 (September 1989) pp 1131-1142 9 Poo, G S and Ang, W 'OSI protocol choices for LAN environments', CompuL Commun., Vol 13 No I (January 1990) pp 17-26 10 ISO 8073 Standard: Connection Oriented Transport Protocol Specification, ISO 1986-07-I 5, ISO, Geneva, Switzerland (I 986) 11 Svobodova, L, lanson, P and Mumprechl, E 'Heterogeneity and OSI', IEEE J. Selected Areas in Commun, Vol 8 No 1 (January 1990) pp 67-79 12 Brady, P T 'Performance of an edge-to-edge protocol in a simulated X.25/X.75 packet network', IEEE J. Selected Areas in Commun., Vol 6 No 1 (January 1988) pp 190-196 13 Collela, R, Aronoff, R and Mills, K 'Performance improvement for ISO transport protocol', ACM Comput. Commun. Rev., Vol 15 No 4 (1985) pp 9-16

computer communications