TCP dynamic acknowledgment delay (extended abstract): theory and practice
WQ study an on-line problem that is motivated by the networking problem of dynamically adjusting delays of acknowlcdgmcnts in the Transmission Control Protocol (TCP). The thcoroticnl problem we study is the following. There is a scqucnco of n packet arrival times .4 = (or,. . . , an) and a look-nhoad coefficient L, The goal is to partition A into 1; subsequences orroe,. . . , a~: (where a subsequence end is deilncd by an acknowledgment) that minimizes a linear combination of the cost for the number of acknowledgments sent and the cost for the additional latency introduced by delaylng acknowledgments. At each arrival, an oracle provides the algorithm with the times of the next L arrivals. First we give an 0(n*) dynamic programming algorithm for optimally solving the off-line problem. Then we deacribc an on-line algorithm that greedily acknowledges exactly when the cost for an acknowledgment is less than the latency cost obtained by not acknowledging. We show that for this algorithm there ls a sequence of n packet arrivals for which it is S-l (fi) -competitive. Next we present a second on-line algorithm which is a slight modification of the first that we prove is 2-competitive. Let Copt be the cost of the optimal solution and let CA be the cost of the solution produced by algorithm A. We then show that for any on-line algorithm A with any constant look-ahead L, CA > SC+-c where c is a factor that can be made arbitrarily small with rcnpcct to Capt. Thus, in the worst case, our result for L = 0 IQ the hcst possible even for on-line algorithms that can use nny constant look-ahead. We then give some initial empirical results using arrival sequences from real network traffic where we compare the two methods used in TCP for acknowledgment delay with our two on-line algorithms. In all cases we examine performance mitli L = 0 and L = 1, Finally, we consider an alternate dcilnition for the latency cost in our objective function, *Supported in part by NSF NY1 Grant CC%9357707 with mntching funds provfdcd by WUTA.