This paper investigates the performance of a single-server queueing model with impatient consumers wherein the server is subject to failures. Two types of services are offered, namely, mandatory service and secondary service. The mandatory service is essential to all the consumers whereas the secondary service is opted by only few consumers after the completion of mandatory service. During the periods of working vacations, service is provided to the waiting consumers, if any, at a reduced rate but not halted. Two types of consumer impatience are incorporated: balking and reneging when the service is not completed within the anticipated time. The model’s steady-state probabilities are determined using the matrix method. An analysis of the key performance metrics such as anticipated system size, anticipated rate of loosing a consumer, etc., is presented. Numerical examples validating the theoretical findings are displayed as graphs.

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Impatient Consumer Queue with Secondary Service, Server Failures and Delayed Working Vacations

  • K. Jyothsna,
  • P. Vijaya Kumar

摘要

This paper investigates the performance of a single-server queueing model with impatient consumers wherein the server is subject to failures. Two types of services are offered, namely, mandatory service and secondary service. The mandatory service is essential to all the consumers whereas the secondary service is opted by only few consumers after the completion of mandatory service. During the periods of working vacations, service is provided to the waiting consumers, if any, at a reduced rate but not halted. Two types of consumer impatience are incorporated: balking and reneging when the service is not completed within the anticipated time. The model’s steady-state probabilities are determined using the matrix method. An analysis of the key performance metrics such as anticipated system size, anticipated rate of loosing a consumer, etc., is presented. Numerical examples validating the theoretical findings are displayed as graphs.