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Modeling and performance issues in routing problems
Abstract
The objective of a routing algorithm in a network is to provide paths from source to destination for each incoming unit of work so as to optimize some appropriate cost function. Many sophisticated routing algorithms are based on distributional assumptions regarding the underlying arrival and service processes at the network nodes. This dissertation examines the effect of uncertainties in modeling the underlying processes on the optimization process. In addition, it explores answers to a related question: is it at all possible to do optimal routing without any modeling assumptions regarding the underlying processes? The effect of modeling uncertainties on the optimization process is examined for a generic basic routing model where each incoming unit is routed to one of several parallel heterogeneous servers, each associated with a queue of infinite capacity, with a certain probability. It is expected that any error in modeling the underlying processes will result in errors in the optimal routing solution and the optimal cost which is chosen to be the optimal mean system delay. For Poisson arrivals some asymptotic properties of the errors due to uncertainties in modeling the service time distribution are derived for heavy traffic conditions. For exponential service time distributions similar asymptotic characterizations of the errors resulting from modeling uncertainties in a General renewal arrival process are also derived. The differences between the two cases are identified and are numerically illustrated. Several model-based and model-independent gradient-based on-line routing algorithms are proposed for the above basic routing model and their performances are compared through simulations for various underlying arrival and service processes. An estimator for the gradient of mean delay on a tandem link (i.e. several queues in tandem) with respect to the routing probability (admission probability) associated with it is developed and using this a gradient-based algorithm is proposed for routing in a system of parallel tandem links. The performance of this algorithm is compared with that of some other model-based and model-independent algorithms through simulations. Finally the performance of a proposed on-line gradient-based routing algorithm is compared with that of two routing algorithms in practice, namely the CODEX Algorithm and the ARPANET Algorithm, by applying them to a communication network model.
Subject Area
Electrical engineering|Industrial engineering|Computer science
Recommended Citation
Mohanty, Bibhu Prasad, "Modeling and performance issues in routing problems" (1993). Doctoral Dissertations Available from Proquest. AAI9408315.
https://scholarworks.umass.edu/dissertations/AAI9408315