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which covers SNA control mechanisms. Other types of congestion control have also been
suggested or used, and some of these will be described later in this chapter. Control mechanisms
are always needed to guard against stochastic fluctuations in traffic that may arise, which may
temporarily deplete network resources (nodal buffers and transmission links) and causecongestion to develop.
When it occurs, congestion manifests itself in two ways: Time delays will increase markedly inthe network, and the throughput, measured in packets per unit time delivered to their
destinations, may begin to decrease as offered load increases. Both effects are diagrammed in
Fig. 5-8. As shown in the figure, the decrease in throughput with an increase in offered load beyond a specified operating point is due to the blocking of finite resources in the network
(buffers and finite line capacity). If an offered load is high enough, a deadlock situation may
even prevail: All buffers are filled, traffic ceases to flow, and the throughput drops to zero.
Strategies have been proposed to prevent the occurrence of deadlock [CIES], [KLEI 1976].Deadlock is not considered explicitly in the viruial circuit window flow-control analysis
described in this section. Rather, it is assumed that the control mechanism eliminates the
congestion region of the throughput curve of Fig. 58; infinite buffer models used for the analysisdo not exhibit the deadlock behavior of that curve. In Section 5 — 5, which cover congestion
control by input-buffer limiting, the phenomenon of deadlock does appear in the model used,
since it incorporates a finite buffer. The use of (more realistic) finite buffers in the VC model of
this section would complicate the analysis immeasurably with little gain in insight.
The purpose here is to compare window control mechanisms on the basis of their time delay-
throughput characteristics. We assume chat these mechanisms, if properly designed, do not letdeadlock develop. To carry out the analysis we first develop a model for the virtual circuit, then
show how the window control mechanism may be easily modeled on top of this.
[GIES] A. Giessler et al., “Flow Control Based on Buffer Classes,” IEEE Trans. on Comm., vol.
COM-29, no. 4, April 1981, 436-443.
[KLEI 1976] L. Kleinrock, Queuing Systems. Volume 2, Computer Applications, John Wiley &Sons, New York, 1976.
5 — 2 — 1 Virtual Grcuit Model
Consider a virtual circuit covering M store-and-forward nodes from source to
destination in a packet-switched network. A typical example appears in Fig.
5 — 9(a). Three virtual circuits are shown in this small network example. All
emanating from the same source node I. VC1 traverses M 3 store-and-for ward
nodes (including the source node), while VC2 and VC3 each cover two store-and-forward nodes. The virtual circuits overlap in three of the network
links. 1f we focus on only one VC, a little thought will indicate that it may
be modeled by the M queues in series of Fig. 5 — 9(b). This is an extension of
the single-queue model for the store-and-forward process at a node in a
network
that was treated in Chapter 2. The parameter). represents. as usual, the
average
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packet-arrival rate (load) to the VC, and Poisson arrival statistics are
assumed.
As was the case previously, this is the simplest model possible: A single
server
(single transmission link) servicês each queue.
Propagation delay has been neglected The two sources of delay in each
queue are thus queueing deLay (wait time) and transmission time. The latter
depends. of course, on packet length and transmission-link capacity. For the
i th
queue in the VC (I I M), the transmission rate or capacity is denoted by p
packets/sec. (The daca link control on each link along a VC is ignored her.
Recall that by virtue of the network layering concept used, the daca link
layer
provides the VC with an error-free, transparent transmission medium on each
link along the path. Occasional bit errors Will cause link frames, and hence
packets within them, to be retransmitted. This phenomenon occurs relatively
infrequently and is assumed to have negligible effect on the VC time delay;
thus
it is ignored. The transparency of che data link layer enables us co decouple
the
characteristics of the two layers.)
A more general (and more valid) model would show the complete network
represented by interconnected queues with virtual circuits superimposed arid
interacting. The analysis of such a queueing network is much mòre complex and
is deferred until Section 5 — 4. It is apparent from Fig. 5 — 9 that even if one
focuses on a single VC. as is the case here, two or more VCs may share nodal
queues arid transmission links, giving rise to queues with multiple
customers.
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180 Network Layec Flow Control and Congestion Control
5 — 2-2 Sliding-window Model
The discussion up to this point has focused on validating the queueing
network model of Fig. 5 — 9(b) for a single virtual circuit. How does one now
superimpose the flow-control mechanism on this model? We describe the
sliding-window control first. Recall from Section 5 — 1 that in this control
mechanism each packet is individually acknowledged as it arrives at its
destination. The acknowledgement, on arriving back at the source, shifts the
window forward by one, allowing another packet to enter the network if all
packets in a window have been previously transmitted. An example appears in
Fig. 5 — 10. We now use the letter N to represent the window size; the letter w
will be used to describe the next window control mechanism that we model and
analyze.
By virtue of the sliding-window control, packetscan be transmitted onto the
VCso long as there are fewer than N along the VC. IfN have already entered
the
VG no more are allowed in until an acknowledgement packet arrives, sliding
the window forward by one. How arriving packets are handled when the window
is depleted (N unacknowledged packets are in transit along the VC) gives rise
to
a variety of control models. We choose the simplest case: Packets are assumed
blocked and lost to the system if, on arrival, N packets are outstanding
along the
VG. This is often a realistic case. Consider two examples. In the first
example,
that of interactive terminals accessing a network, terminal keyboards might
be
locked under conditions of congestion. The user must wait until a later time
to
transmit his or her data. The packets he or she might have transmitted are
thus
• Figure.5— 9 Single virtual circuit model
a. Virtual circuits in a network
b. Virtual circuit queueing model
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Figure 5 — 9(b) thus should really show multiple customer streams arriving at
various queues along the VC and exiting as they move along their own VC. The
simplest model that takes these added customer types into account assumes
that
they use up a portion of the transmission capacity on a given link, reducing
the capacity available to the VC user. This concept is made more rigorous and
is
justified mathematically in [PENN] and (SCHW 19771. The s shown in Fig.
5 — 9(b) are assumed to have been reduced accordingly.
(PENN] M. C. Pennotti and M. Schwartz. “Congestion Control in Store and
Forward
Tandem Links,” IEEE Tran.m. on Cornu., vol. COM-23, no. 12, Dec. 1975, 1434 —
1443.