**Mor Harchol-Balter and Paul E. Black**,
*Queuing Analysis of Oblivious Packet-Routing Networks*,
Proceedings of the 5th ACM-SIAM
Symposium on Discrete Algorithms (SODA '94), Washington, D.C., USA
(January 1994), ACM, 1994, pages 583-592.

**Abstract**:- We consider the problem of determining the probability distribution on the queue sizes in a general oblivious packet-routing network. We assume packets continuously arrive at each node of the network according to a Poisson process with rate lambda. We also assume that an edge may be traversed by only one packet at a time, and the time to traverse an edge is an exponentially distributed variable with mean 1.
- We show that the queuing-theoretic solution to the problem requires solving a large system of simultaneous equations.
- We present a simple combinatorial formula which represents the solution to the system of queuing equations. This combinatorial formula is especially simple and insightful in the case of greedy routing to random destinations.
- We use the formula to obtain results including: the probability distribution on the queue sizes, the expected queue sizes, and the expected packet delay (all as a function of lambda) in the case of an array network and a torus network with greedy randomized routing.

Get the paper in Postscript (190k) or PDF (222k). Expanded version with application to tori in Postscript (203k) or PDF (226k).

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