Abstract
In this paper we discuss a queueing system with service interruption. The service gets interrupted due to different environmental factors. Here it is assumed that interruption due to only one factor is allowed at a time. Further we assume that while in interruption no other interruption befalls the system. Even though any number of interruptions can occur during the service of a customer, the maximum number of interruptions is restricted to a finite number K and if the number of interruptions exceeds the maximum, the customer leaves the system without completing service. The difference between the model under discussion and those considered earlier in literature is that the customer/server is unaware of the interruption until a random amount of time elapses from the moment interruption strikes. At the moment the interruption occurs, a random clock and a superclock start ticking. The interruption is identified only when the random clock is realized. The superclock measures the total interruption time during the service of a customer. On realization of superclock the customer goes out of the system without completing service. The kind of service to be started after the interruption depends on the environmental factor that caused the interruption. Here we first analyze the service process to find the response time and to compute the stability condition. The optimal values of K for a suitable cost function is investigated. Numerical investigations indicates the cost function as convex/increasing/decreasing in K.
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The authors thank the reviewers for the valuable suggestions which helped in improving the presentation of the paper.
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The research was supported by Kerala State Council for Science, Technology and Environment (No. 001/KESS/2013/CSTE) and FDP of UGC (No. F.FIP/12th Plan/KLMG009 TF-12).
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Krishnamoorthy, A., Jaya, S. & Lakshmy, B. Queues with interruption in random environment. Ann Oper Res 233, 201–219 (2015). https://doi.org/10.1007/s10479-015-1931-4
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DOI: https://doi.org/10.1007/s10479-015-1931-4