Sec.6.2 Window Flow Control 501 the transmission rate of the session.For example,the receiver may do so to avoid buffer overflow. In the subsequent discussion,we consider two strategies,end-to-end and node-by- node windowing.The first strategy refers to flow control between the entry and exit subnet nodes of a session,while the second strategy refers to flow control between every pair of successive nodes along a virtual circuit's path. 6.2.1 End-to-End Windows In the most common version of end-to-end window flow control,the window size is alf',where a and II'are some positive numbers.Each time a new batch of a data units is received at the destination node,a permit is sent back to the source allocating a new batch of a data units.In a variation of this scheme,the destination node will send a new a-data unit permit upon reception of just the first of an a-data unit batch.(See the SNA pacing scheme description in Section 6.3.)To simplify the following exposition, we henceforth assume that a =1,but our conclusions are valid regardless of the value of a.Also,for concreteness,we talk in terms of packets,but the window maintained may consist of other data units such as bytes. Usually,a numbering scheme for packets and permits is used so that permits can be associated with packets previously transmitted and loss of permits can be detected.One possibility is to use a sliding window protocol similar to those used for data link control, whereby a packet contains a sequence number and a request number.The latter number can serve as one or more permits for flow control purposes (see also the discussion in Section 2.8.2).For example,suppose that node A receives a packet from node B with request number k.Then A knows that B has disposed of all packets sent by A and numbered less than k,and therefore A is free to send those packets up to number +-I that it has not sent yet.where W'is the window size.In such a scheme,both the sequence number and the request number are represented modulo m,where m >I+1. One can show that if packet ordering is preserved between transmitter and receiver,this representation of numbers is adequate;the proof is similar to the corresponding proof for the goback n ARQ system.In some networks the end-to-end window scheme is combined with an end-to-end retransmission protocol,and a packet is retransmitted if following a suitable timeout,the corresponding permit has not returned to the source. To simplify the subsequent presentation,the particular manner in which permits are implemented will be ignored.It will be assumed that the source node simply counts the number of packets it has already transmitted but for which it has not yet received back a permit,and transmits new packets only as long as r W. Figure 6.6 shows the flow of packets for the case where the round-trip delay d, including round-trip propagation delay,packet transmission time,and permit delay is smaller than the time required to transmit the full window of W packets,that is, d≤IIX where X is the transmission time of a single packet.Then the source is capable of transmitting at the full speed of 1/X packets/sec,and flow control is not active.(ToSec. 6.2 Window Flow Control 501 the transmission rate of the session. For example, the receiver may do so to avoid buffer overflow. In the subsequent discussion, we consider two strategies, end-fa-end and node-by￾node windowing. The first strategy refers to flow control between the entry and exit subnet nodes of a session, while the second strategy refers to flow control between every pair of successive nodes along a virtual circuit's path. 6.2.1 End-to-End Windows In the most common version of end-to-end window flow control, the window size is on-, where a and n° are some positive numbers. Each time a new batch of a data units is received at the destination node, a permit is sent back to the source allocating a new batch of a data units. In a variation of this scheme, the destination node will send a new a-data unit permit upon reception of just the first of an Q-data unit batch. (See the SNA pacing scheme description in Section 6.3.) To simplify the following exposition, we henceforth assume that 0 = I, but our conclusions are valid regardless of the value of a. Also, for concreteness, we talk in terms of packets, but the window maintained may consist of other data units such as bytes. Usually, a numbering scheme for packets and permits is used so that permits can be associated with packets previously transmitted and loss of permits can be detected. One possibility is to use a sliding window protocol similar to those used for data link control, whereby a packet contains a sequence number and a request number. The latter number can serve as one or more permits for flow control purposes (see also the discussion in Section 2.8.2). For example, suppose that node A receives a packet from node B with request number k. Then A knows that B has disposed of all packets sent by A and numbered less than k, and therefore A is free to send those packets up to number k+ W - I that it has not sent yet, where VV is the window size. In such a scheme, both the sequence number and the request number are represented modulo Tn, where Tn 2 TV +1. One can show that if packet ordering is preserved between transmitter and receiver, this representation of numbers is adequate; the proof is similar to the corresponding proof for the goback n ARQ system. In some networks the end-to-end window scheme is combined with an end-to-end retransmission protocol, and a packet is retransmitted if following a suitable timeout, the corresponding permit has not returned to the source. To simplify the subsequent presentation, the particular manner in which permits are implemented wiIl be ignored. It will be assumed that the source node simply counts the number ~. of packets it has already transmitted but for which it has not yet received back a permit, and transmits new packets only as long as x: < VV. Figure 6.6 shows the flow of packets for the case where the round-trip delay d, including round-trip propagation delay, packet transmission time, and permit delay is smaller than the time required to transmit the full window of VV packets, that is, where X is the transmission time of a single packet. Then the source is capable of transmitting at the full speed of 1/X packets/sec, and flow control is not active. (To