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An Approximation of the M/G/1 System with Finite Workload Capacity  

Lee, Hyung Joong (Department of Industrial Engineering Hanyang University)
Hur, Sun (Department of Industrial Engineering Hanyang University)
Publication Information
Journal of Korean Institute of Industrial Engineers / v.29, no.3, 2003 , pp. 247-252 More about this Journal
Abstract
We propose an approximation of the M/G/1 system with finite workload capacity, where those customers whose admission to the system would increase the workload beyond a prespecified finite capacity limit are not accepted. Our approximation method is based on the idea that the service time of a customer in the M/G/1 system can be approximated as the sum of service times of a batch of customers in the $M^X/d/1$ system where the deterministic service time d is small enough. That is, the original service time is discretized and approximated by the batch size. We exemplified our method by obtaining the average workload of the M/M/1 system by means of the $M^X/d/1$ system, where the batch size is geometric. In addition, the approximate blocking probabilities of the M/M/1 and $M/E_k/1$ system with finite workload capacities are sought. The proposed method turns out to give a good approximation, which is compared with a simulation.
Keywords
finite capacity; MIG/1; total rejection; blocking probability;
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