Mirchevski, Stefan
Preferred name
Mirchevski, Stefan
Official Name
Mirchevski, Stefan
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Item type:Publication, Cost Parameters-Based Comprehensive Analysis of a New Cost Function Construction for Coxian-k Queueing System Characterized by Customer Service Speed Variability(MDPI AG, 2026-03-06); ; We investigate cost optimization in an 𝑀/Cox𝑘/1 queueing system with phase-dependent service speeds. A unified parametric framework is introduced to model both homogeneous and heterogeneous service regimes, and closed-form expressions for steady-state performance measures are derived. These results are used to construct an expected total cost function explicitly parameterized by the traffic intensity. We prove that the cost function is strictly convex on the stability region, ensuring the existence and uniqueness of the optimal traffic intensity. For the Coxian-2 case, analytical and numerical sweep analyses are conducted with respect to waiting and service-capacity cost parameters. Polynomial response surfaces and nonparametric statistical tests are employed to validate the robustness of the results. The analysis shows that balanced service speeds across phases consistently yield lower optimal traffic intensity levels and reduced expected total costs, whereas heterogeneous service speeds increase congestion and cost sweep. These findings provide practical guidance for the economic design and control of multi-phase service systems. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Construction and Optimization of a Cost Function in a Single‐Server Multiphase Queueing System With Hypoexponential‐
<i>k</i>
Customer Service Time(Wiley, 2026-01); ; ; Hazra, ArpanIn this paper, a new generalized cost function construction for a single-server multiphase queueing system with a Poisson input stream, hypoexponential-k customer service time, and FIFO discipline is presented. A proposed relationship between service parameters in k phases is based on a geometric progression with rate α, 0 < α < 1. In this way, an approach with a constantly decreasing speed of servicing customers through the phases is introduced. Several auxiliary lemmas about the performance measures of the proposed model are proved. Then, an explicit form of the cost function is obtained in such a construction, expressed as a function of the traffic intensity ρ. Also, an analysis of the cost function is made, and a theorem for the existence and uniqueness of the absolute minimum of the cost function is proved. Furthermore, a sensitivity analysis of the optimal solutions with different changes in the cost values, input stream parameter, and progression rate α is additionally made.