are obtained for performance of interest such as throughput and channel activity, both in the case of selective and non- selective reject modes of operation in the ...
Performance Evaluation of the HDLC Protocol Erol Gelenbe L.R.L, Universitd Paris-Sud, Centre d'Orsay, 91405 Orsay, France
and
Erol Gelenbe was born in Instanbul (Turkey) in 1945, and he obtained his undergraduate engineering degree from the Middle East Technical University in Anakara. After receiving the Master's and Ph.D (1969) degrees from the Polytechnic Institute of Brooklyn in Electrical Engineering he joined the faculty of the University of Michigan (Ann Arbor). In Ann Arbor, he taught graduate and undergraduate courses in various areas of computer science, including programming languages and data structures, compiler design, operating systems and system performance evaluation. Although his early papers are on stochastic automata theory, most of Dr. Gelenbe's publications concern the performance evaluation of largescale computer systems. In 1973 he was awarded the Doctorat d'Etat degree from the Universite Paris VI. Since 1972 he has been associated with LABORIA/IRIA. Le Chesnay, France, where he developed the research activities in modelling and performance evaluation of computer systems, and he presently heads a group working in this area. Since 1973 he has been on the faculty of the Universit6 ParisNord, Villetaneuse, France, where he teaches various computer science topics. From October 1974 to September 1976 he occupied the chair of computer science at the Universitd de Lieg6(Belgium). His present interests include the effect of operating system structure on system performance, the analysis of computer system reliability, problems related to memory management, and the performance evaluation of computer commtlnication systems.
Jacques Labetoulle and Guy Pujolle, IRIA-Laboria B.P. 105, 78150 Le Chesnay, France The HDLC (High-Level Data Link control) protocol has been accepted as an international standard for computer communications. As such it is very important that its performance limits be well understood. The mathematical model of HDLC developed in this paper allows us to compute its performance limits as a function of window width, transmission errors, and packet lengths for symmetric and asymmetric traffics, but with no transmission delays. Explicit formulas are obtained for performance of interest such as throughput and channel activity, both in the case of selective and nonselective reject modes of operation in the presence of errors.
Keywords: Performance prediction, Queuing networks, Transaction processing, Node-node protocols, HDLC protocol
Jacques Labetoulle was born in Grenoble (France) in 1946. He obtained an engineering degree from the Ecole Centrale des Arts et Manufactures in 1970 and the Doctorat de 3~me cycle degree in 1974. He entered IRIA in 1971 and joined the computer system modelling group. His interests include the modelling of special purpose networks such as loop networks and satellite links like ALOHA, and the study of approximate solutions tor large networks of queues. Beside his interests in networks, he has studied some deterministic scheduling problems and has published several papers on that subject. Guy Pujolle was born in 1949 in Paris. He obtained his Maitrise de Math6matiques from Universit6 Paris VII in 1972. After graduate work in probability theory at Universit6 Paris VI, he joined the research group on Computer System modelling at IRIA/ LABORIA and obtained his Doctorat de Troisi~me Cycle degree in february 1975. The subset of his works is the analysis of networks of queues with finite capacity and blocking using some approximation techniques, and the application of these results to multiprogramming systems and to computer networks. Dr. PUJOLLE has published several papers in this and related areas. He is presently interested in protocols, and in the performance prediction of computer networks.
This paper has been presented at the Computer Network Protocols Symposium, held in Liege (Belgium) in February 1978 and organized by the University of Liege. The permission to reprint this paper is gratefully acknowledged. 1 High level data link control (HDLC) procedures are designed to permit synchronous bit sequence independent transmission. © North-Holland Publishing Company Computer Networks 2 (1978) 409-415 409
E. Gelenbe et al. / Performance evaluation of the HDL C protocol
410
1. Introduction
mum number of unacknowledged packets which node i is allowed to send before it must stop and wait for an acknowledgement. Then we shall say that Ni is the window width o f node i. Thus, the simple SW protocol has a window width of 1 for all nodes. Throughout the paper we shall consider two nodes, 1 and 2, communicating with each other and assume that each node has an infinite stream of packets to send to the other node. We will obtain an explicit formula for the maximum throughput of the two-way channel as a function of the window width at each node, of the packet lengths, and of the length of the acknowledgements. Our model is an accurate representation of the satured behaviour of the protocol HDLC and can serve as a means for "tuning" the protocol by proper choice of parameters.
There has been considerable interest recently in the definition of international computer communication protocols [1] and in the technical and political issues which surround them. The performance evahlation of these protocols has lagged somewhat behind, though considerable progress has been made in understanding the aspects which influence their behaviour
[2,3,4]. In a recent paper [3] the performance limits, in maximum achievable throughput, for a simple SendAnd-Wait (SW) procedure have been derived using a mathematical model and the results confirmed by measurements on an implemented version of the protocol. In [4] the behaviour of an SW protocol has been analysed in the presence of packet loss and of a time-out mechanism to trigger retransmission of packets; the analysis allows us to determine the optimum time-out duration in order to minimize transit delays through a node, or packet loss at a finite buffer, or to maximize the throughput of a node. The purpose of this paper is to evaluate the performance of the HDLC 1 window width protocol. Consider two nodes, or processes (in the usual computer science terminology a process is a program during its execution), communicating with each other along two parallel channels. Suppose that each channel is used for transmitting packets going in each direction, including acknowledgement packets. Suppose that node i ( i = l or 2) will send up to N i packets to its partner before stopping and waiting for an acknowledgement; in other words, Ni is the maxi-
2. The behaviour of the protocol We show schematically the behaviour of the two nodes under the influence of the protocol we shall analyse in fig. 1. Each node has an infinite queue of packets waiting to be sent to the other node. The channel is represented by a transfer time from the transmitting node to the receiving node; it is assumed that the reception and "consumption" of the packet by the receiving node takes place as soon as the transmission ends. Thus we are neglecting the hardware and software delays which take place at the packet switching node. Equivalently, we can assume that these delays are incorporated in the transmission
N2
I
III
Packet
Packet
arrivals
arrivals
N1
~-
Fig. 1. Behaviour of the protocol.
E. Gelenbe et al. /Performance evaluation of the HDLC protocol delay. As soon as a packet transmission ends, the transmitting node does not destroy its copy of the packet: it places it in a queue of packets which it has transmitted but which have not yet been acknowledged. These queues will be called Q1 at node 1 and Q2 at node 2. As soon as Q1 contains N1 packets, node 1 stops transmitting packets to node 2: its transmissions will begin again as soon as the length of Q1 decreases below N1. Each time a packet is acknowledged it is removed from Q1. The behaviour o f node 2 is symmetrical. In this section we exclude the effects of packet loss of errors. That is we assume that each packet transmitted will eventually be acknowledged. The assumption is reasonable if packet loss or transmission errors are negligible. Indeed, we shall see that the window width has a first order effect on the throughput of the two-way communication, while in normal operation unacknowledged packets are rare. The effect of packet loss will be examined in Section 4, where it will be assumed that each packet travelling from 1 to 2 may be lost independently of other packets with probability Pl (P2 for the other direction). We shall make two types of assumptions concerning the acknowledgement (ACK) messages: (i) The ACK is contained in each packet, so that each arriving packet to node 1 from node 2 contains an ACK for all of the packets contained in Q I , and vice versa. (ii) The ACK is only recognized after the whole packet which carries it has been received.
3. The model of HDLC In this section we shall present a model for the behaviour of the HDLC protocol for arbitrary N1 and N2. It will be assumed that no packet loss or errors occur and that both riodes have an infinite stream o f packets to send to the other node. The protocol is modelled by the state diagram of Figure 2. The protocol is in state (i,j) if node 1 has transmitted i packets and these have not yet been acknowledged. That is, state (i,j) corresponds to the case where Q1 contains i packets, Q2 contains/. packets. Node 1 is transmitting its i + lth packet and node 2 is transmitting its/. + lth packet in state (i,/.) if i < N1,/. < N 2 . In state (NI,/'), node 1 has stopped transmitting; the same is true of node 2 in state
(i, Nz).
411
j
Fig. 2. State transitions for the HDCLL protocol.
We immediately see that the only possible states for the system are (0, 0), (0, 1) ..... ( 0 , / ~ ) , ( 1 , 0 ) ..... (?¢1,0) since as soon as a packet is received by a node the node also receives an ACK for all packets it has sent and which have not yet been acknowledged. We shall assume that packets going from node 1 to node 2 are of exponentially distributed length of average value X, while the same assumption is made for the portion of packet length associated with the ACK we assume that X = x + A , Y = y + A , where A is the length of the portion of a packet reserved for ACK's. We will also suppose that the link speed in both directions is the same and that the time for transmission of a packet is given by the packet length (or, equivalently, that we express packet length in terms of transmission time). The state transitions for the HDLC protocol are shown in fig. 2. A transition from state (0,j) to (0,/" + 1) occurs because the transmission from node 2 to node 1 ends before the transmission from node 1 to node 2. Since the packet lengths are exponentially distributed, the probability of this transition is simply X / ( X + If) due to the memoryless property of the exponential distribution. Similarly, the probability of a transition from (i, 0) to (i + 1,0) is Y / ( Y + X). Suppose that in state (i, 0) the transmission from node 1 to 2 completes before the ongoing transmission from 2 to 1. Then the protocol will enter state (0, 1) since all unacknowledged packets at node 1 will have been acknowledged, while there will now be an unacknowledged packet in Q2. This transition will take place with probability X/~(X + II). Again, due to the memoryless property of the
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E. Gelenbe et al. / Performance evaluation of the HDL C protocol
exponential distribution, the time spent by the protocol in state (i, O) is the smaller one of the two transmission times (from 1 to 2 and from 2 to 1); as such, it is exponentially distributed of average value (X -1 "l" y-X)-1. Of course, the same is true for state (0, D. The residence time in state ( N 1 , 0 ) i s exponentially distributed of mean Y, and for state (0, N2) it is exponentially distributed of mean X. The model of the protocol we have defined is therefore a finite-state Markov chain. We see that the state (0,0) is transient, since once this state has been left it is impossible to enter it once again. The remaining states form an irreducible class. Let us first compute the stationary (long-run) probabilities associated with this chain. We shall denote ui the stationary probability of being in state (i, 0) and vl the stationary probability of state (0,]). The equations satisfied by these probabilities are then
Ul = Vl = X Y / ( X + y)2 , UN1
=( y ]Nx \X + Y/
'
Ul(x+l)=uo/X+~oj/X
(1)
ON2
= ( X ~N2 \X + Y/ "
(7)
The primary performance measure which will be of interest to us in this paper is the throughput of the protocol, or the number of packets transmitted by the channel per unit time. This quantity is defined in terms of channel activity. We define tl, t2 as the activity of channel 1 (node 1 to node 2) and of channel 2 (node 2 to node 1) respectively. The activity of a channel is simply the stationary probability that the channel is busy transmitring a packet. Therefore we have:
tl = 1 -- UN1 ,
t2 = 1 -
(8)
ON2 .
1"i = t l / X
(9)
while for channel 2 it is
N1
(2)
=uo/Y + ]~]ui/Y 1
where we have denoted by Uo the stationary probability of state (0, 0). Since this state is transient it follows that Uo = 0. The reamining equations are:
I"2 = t d r .
(lo)
In order to account for the overhead introduced by ACK pacekts, we shall define the effective activity t e l , te2 : tel = t l X / Y ,
ui(1-1-1)=Ui_l/X,
v/(~+l)=vj_l/Y,
for 1 < i < N 1 ,
Finally,
1
