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Cost function analysis of a single-server queueing system with Poisson input stream and Erlang-k service time

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  • Mirchevski, Stefan
  • Bakeva, Verica

Abstract

In this paper, the cost function of a single-server queueing system with Poisson input stream and Erlang-k service time will be analyzed. Treated as a function of the traffic intensity ρ, with respect to some known constants, we will show that its stationary points are solutions of a fourth-degree polynomial equation with real coefficients. Moreover, an explicit form of these solutions is given and it is shown the function reaches a minimum value at some of these points. For illustration, a numerical analysis of the cost function is carried out by changing the values of the costs, which are changed according to the principle of arithmetic progression. Also, a statistical analysis of the relationship between optimal solutions ρ⁎ and Φ(ρ⁎) is done.

Suggested Citation

  • Mirchevski, Stefan & Bakeva, Verica, 2024. "Cost function analysis of a single-server queueing system with Poisson input stream and Erlang-k service time," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    • Handle: RePEc:eee:apmaco:v:475:y:2024:i:c:s0096300324002017
    DOI: 10.1016/j.amc.2024.128729
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    References listed on IDEAS

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