Constant Time per Edge is Optimal on Rooted Tree Networks

We analyze the relationship between the expected packet delay in rooted tree networks and the distribution of time needed for a packet to cross an edge using convexity-based stochastic comparison methods. For this class of networks, we extend a previously known result that the expected delay when the crossing time is exponentially distributed yields an upper bound for the expected delay when the crossing time is constant 20] using a di erent approach. An important aspect of our result is that unlike most other previous work, we do not assume Poisson arrivals. Our result also extends to a variety of service distributions, and it can be used to bound the expected value of all convex, increasing functions of the packet delays. An interesting corollary of our work is that in rooted tree networks, if the expectation of the crossing time is xed, the distribution of the crossing time that minimizes both the expected delay and the expected maximum delay is constant. Our result also holds in m...

• Type: Conference
• Year: 1996
• Where: SPAA
• Authors: Michael Mitzenmacher
• Keywords: Distributed And Parallel Computing, Packet Delays, Rooted Tree Networks, SPAA 1996, Stochastic Comparisons