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International Conference on Mathematics and Computing

ICMC 2018: Mathematics and Computing pp 23–42Cite as

A Dynamic Non-preemptive Priority Queueing Model with Two Types of Customers

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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 253)

Abstract

In this paper, we study a single-server non-preemptive priority queueing model with two types of customers. The customers arrive according to two independent Poisson processes, and the service times are exponential with possibly different parameters. While Type 1 customers, who have non-preemptive priority over Type 2 customers, have a finite waiting room, Type 2 customers have no such restriction. A new dynamic rule based on a predetermined threshold is applied in offering services to lower-priority customers (when higher-priority customers are present) whenever the server becomes free. Using matrix-analytic methods, we analyze the model in steady state and bring out some qualitative and interesting aspects of the model under study. We also compare our model to the classical two-customer non-preemptive priority model to show a marked improvement in the quality of service to customers under the proposed threshold model.

Keywords

  • Queueing
  • Dynamic non-preemptive priority
  • Matrix-analytic method
  • Algorithmic probability

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Authors and Affiliations

  1. Departments of Industrial and Manufacturing Engineering & Mathematics, Kettering University, Flint, MI, 48504, USA

    Srinivas R. Chakravarthy

Authors
  1. Srinivas R. Chakravarthy
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Corresponding author

Correspondence to Srinivas R. Chakravarthy .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India

    Prof. Debdas Ghosh

  2. Department of Computer Science and Engineering, Haldia Institute of Technology, Haldia, West Bengal, India

    Prof. Debasis Giri

  3. Department of Mathematics, University of Central Florida, Orlando, FL, USA

    Prof. Ram N. Mohapatra

  4. Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka, Japan

    Prof. Kouichi Sakurai

  5. Uşak University, Uşak, Turkey

    Prof. Ekrem Savas

  6. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India

    Prof. Tanmoy Som

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Chakravarthy, S.R. (2018). A Dynamic Non-preemptive Priority Queueing Model with Two Types of Customers. In: Ghosh, D., Giri, D., Mohapatra, R., Sakurai, K., Savas, E., Som, T. (eds) Mathematics and Computing. ICMC 2018. Springer Proceedings in Mathematics & Statistics, vol 253. Springer, Singapore. https://doi.org/10.1007/978-981-13-2095-8_3

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