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Optimal control and analysis of bulk service queueing systems
Abstract
Queueing Theory has been successfully and extensively applied to the scheduling, control, and analysis of complex stochastic systems. In this dissertation, the problems of optimal scheduling, control and analysis of bulk service queueing systems are studied. A Dynamic Programming formulation is provided for the optimal service strategy of a two-server bulk queue. An extension of the general bulk service rule is shown to be optimal in the sense of minimizing either the finite discounted or average waiting cost. It is shown that the optimal dispatching rule is a multi-stage threshold type where servers are dispatched only when the number of waiting customers exceeds certain threshold values depending both on the number of waiting customers and the number of servers available at decision epochs. It is conjectured that the result is extendable to the case for more than two servers. Exact analysis of the state probability in equilibrium is carried out under the optimal policy obtained for a queue with two bulk servers. Comparison of the optimal threshold policy is carried out by evaluating a single stage vs. a two-stage threshold two-server system. By calculating the mean number of customers waiting in the queue of both systems, it is shown that a two-stage threshold policy yields optimal performance over the general bulk service rule under any operating condition. Examples for different parameter sets are provided. A network of two bulk service queues served by a common transport carrier with finite capacity is analyzed where the general bulk service rule is applied only at one queue. Decomposition is employed to provide an exact analysis of the steady-state probability distribution, mean waiting time distribution, and mean number of customers waiting at both queues in equilibrium. Networks of more than two bulk service queues can be analyzed by direct extension of the methodology. An optimization procedure for the optimal threshold value to minimize total mean waiting cost is also discussed.
Subject Area
Operations research|Systems science|Computer science
Recommended Citation
Han, Youngnam, "Optimal control and analysis of bulk service queueing systems" (1992). Doctoral Dissertations Available from Proquest. AAI9305834.
https://scholarworks.umass.edu/dissertations/AAI9305834