Models for Optimal Routing in Message Switched and Cell Relay Networks with Time Restrictions

This paper analyzes the problem of determining the primary routes used by two priority classes of messages or cells for each communicating origin—destination (O/D) pair in message switched and Asynchronous Transfer Mode (ATM) networks. The networks are modeled as M/M/ 1a ndM x /D/1 priority queues with two priorities. The goal is to determine routes that satisfy time constraints for communicating pairs with high priority messages. These are taken as the Quality of Service guarantees (QoS). No time constraints exist for the sessions in the second (low priority) class. The problem is formulated as an integer problem and lower bounds on the optimal solution are obtained by Lagrangean relaxation embedded in a subgradient optimization procedure. O/D time restrictions are handled through an augmented Lagrangean procedure. A heuristic method generates routing satisfying time restrictions. The first set of numerical experiments show that M/M/1 without time restrictions has shorter maximum delays in class 1 and longer maximum delays in class 2 than the one with time restrictions. The second set of numerical experiments show that message switching results in lower total cost and queuing delay than the ATM networks under full reliability assumption.

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