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Multiserver Retrial Queues With Two Types Of Nonpersistent Customers

Author

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  • TUAN PHUNG-DUC

    (Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama, Tokyo 152-8552, Japan)

Abstract

We consider M/M/c/K (K ≥ c ≥ 1) retrial queues with two types of nonpersistent customers, which are motivated from modeling of service systems such as call centers. Arriving customers that see the system fully occupied either join the orbit or abandon receiving service forever. After an exponentially distributed time in the orbit, each customer either abandons the system forever or retries to occupy a server again. For the case of K = c = 1, we present an analytical solution for the generating functions in terms of confluent hypegeometric functions. In the general case, the number of customers in the system and that in the orbit form a level-dependent quasi-birth-and-death (QBD) process whose structure is sparse. Based on this sparse structure, we develop a numerically stable algorithm to compute the joint stationary distribution. We show that the computational complexity of the algorithm is linear to the capacity of the queue. Furthermore, we present a simple fixed point approximation model for the case where the algorithm is time consuming. Numerical results show various insights into the system behavior.

Suggested Citation

  • Tuan Phung-Duc, 2014. "Multiserver Retrial Queues With Two Types Of Nonpersistent Customers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-27.
    • Handle: RePEc:wsi:apjorx:v:31:y:2014:i:02:n:s0217595914400090
    DOI: 10.1142/S0217595914400090
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    Cited by:

    1. Nesrine Zidani & Natalia Djellab, 2024. "Asymptotic upper bounds for an M/M/C/K retrial queue with a guard channel and guard buffer," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 99(3), pages 365-407, June.
    2. Phung-Duc, Tuan, 2015. "Asymptotic analysis for Markovian queues with two types of nonpersistent retrial customers," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 768-784.

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