Service Guarantees for Window Flow Control

After presenting some new insight into the concept of \service curves," we derive a \service curve guarantee" for a window ow control protocol with cross-traac characterized by burstiness constraints. Our approach is convenient for studying the end-to-end behavior of hop-by-hop window ow control, and has an interesting relationship with a linear feedback system under the \min-plus" algebra. For aane burstiness constraints on the cross-traac, we nd that a window size proportional to the sum of the burstiness parameters of the cross-traac and the user bandwidth delay product is suucient to maximize guaranteed throughput. In addition, we nd that buuers need not be as large as window sizes for lossless operation with large propagation delays. 1 System Model We will consider the two server system depicted in Figure 1, which models a window ow protocol. Traac from a source is generated according to a function of time R 0 , called a rate function, such that R 0 (t) is the instantaneous rate at which traac is being generated at time t. The traac from the source feeds a buuer, called the rst buuer. Traac departs the rst buuer according to the rate function R 1. We assume that the system is empty at time 0. Let B 1 (t) denote the amount of traac held in the rst buuer at time t. Thus B 1 (t) = Z t 0 R 0 ()dd ? Z t 0 R 1 ()dd : (1) A server, called the rst server, governs the rate R 1 at which traac departs the rst buuer. The server has a transmission capacity of C bits/sec, so that R 1 (t) C for all t. In fact, the rst server handles other sources of traac, called \cross-traac," at time t at rate I 1 (t), where 0 I 1 (t) C; thus R 1 (t) C ? I 1 (t). Traac departs the rst buuer at rate R 1 (t) and feeds a \network element", N f , which serves traac in a FIFO manner at rate R f (t). Recalling that the system is empty at time 0, the amount of traac held in N f at time t is thus B f (t) = Z t 0 R 1 ()dd ? Z t 0 R f ()dd : (2) Network element N f feeds another buuer, called the second buuer. Traac departs the second buuer …