Strategic Joining in an M/M/1 Constant Retrial Queue with Reserved Idle Time Under N-Policy

  • Jinting WangEmail author
  • Lulu Li
Part of the Communications in Computer and Information Science book series (CCIS, volume 1102)


This paper considers an M/M/1 constant retrial queueing model with reserved idle time under N-policy. A customer can occupy the server instantaneously when the server is turned on and idle upon arrival. After the service of the last customer, the server stays idle for some random time. During this period, if a customer arrives, he obtains service immediately. Otherwise, the sever will shut down for saving energy and be reactivated if the number of waiting customers in retrial orbit reaches a given threshold \(N(N>1)\). The probabilities of the server in different states are derived through generating function method. Moreover, based on the reward-cost function and the expected payoff, all customers will decide whether to join or balk the system upon arrival. Given these strategic behaviors we establish the net profit of the service provider per unit of time. Finally, some numerical examples are presented to illustrate the necessity of the reserved idle time’s existence from the perspective of the service provider. It is found the longer the reserved idle time, the greater the server’s profit.


Retrial queue Reserved idle time N-policy Equilibrium strategies 


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Management Science and EngineeringCentral University of Finance and EconomicsBeijingPeople’s Republic of China
  2. 2.Department of MathematicsBeijing Jiaotong UniversityBeijingPeople’s Republic of China

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