Analysis of multi-server queues with station and server vacations |
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| Affiliation: | 1. Department of Industrial and Manufacturing Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA;2. Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, Man., Canada R3B 2 E9;1. Data61, CSIRO, Australia;2. School of Software, Shanghai Jiao Tong University, China;3. National Computational Infrastructure, Australia;4. University of New South Wales, Australia;1. Centre for Healthcare Operations Improvement and Research, University of Twente, Enschede, The Netherlands;2. Department of Donor Studies, Sanquin Blood Supply, Amsterdam, The Netherlands;3. Stochastic Operations Research, University of Twente, Enschede, The Netherlands;1. Centre for Healthcare Operations Improvement and Research, University of Twente, Enschede, The Netherlands;2. Donorstudies, Sanquin Research, Amsterdam, The Netherlands;3. Stochastic Operations Research, University of Twente, Enschede, The Netherlands;4. Department of Public Health, Academic Medical Center, Amsterdam, The Netherlands |
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| Abstract: | In this paper, we consider GI/M/c queues with two classes of vacation mechanisms: Station vacation and server vacation. In the first one, all the servers take vacation simultaneously whenever the system becomes empty, and they also return to the system at the same time, i.e., station vacation is a group vacation for all servers. This phenomenon occurs in practice, for example, when the system consists of a set of machines monitored by a single operator, or the system consists of inseparable interconnected parallel machines. In such situations the whole station has to be treated as a single entity for vacation when the system is utilized for a secondary task. For the second class of vacation mechanisms, each server takes its own vacation whenever it complexes a service and finds no customers waiting in the queue, which occurs, for instance in the post office, when each server is a relatively independent working unit, and can itself be used for other purposes. For both models, we derive steady state probabilities that have matrix geometric form, and develop computational algorithms to obtain numerical solutions. We also analyze and make comparisons of these models based on numerical observations. |
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