Acyclic fork-join queuing networks
Journal of the ACM (JACM)
Average case analysis of greedy routing algorithms on arrays
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
The efficiency of greedy routing in hypercubes and butterflies
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Bounds on the greedy routing algorithm for array networks
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
Bounding delays in packet-routing networks
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Greedy dynamic routing on arrays
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
The power of two choices in randomized load balancing
The power of two choices in randomized load balancing
Stochastic comparisons for rooted butterfly networks and tree networks, with random environments
Information Sciences: an International Journal
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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 different 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 fixed, the distribution of the crossing time that minimizes both the expected delay and the expected maximum delay is constant. Our result also holds in multicasting rooted tree networks, where a single message can have several possible destinations.Besides offering a useful analysis on this restricted class of networks, we also provide a small improvement to the bounding technique. Surprisingly, this improvement is also applicable to previously developed comparison methods, leading to an improvement in the upper bounds for greedy routing on butterfly and hypercube networks given by Stamoulis and Tsitsiklis [20].