Sep 2026· Applied Stochastic Models in Business and Industry· 0 citations· 18 references
TL;DR
This paper investigates the steady‐state performance of an queueing system subject to random and time‐homogeneous partial and complete server breakdowns and develops a structured cost model to account for service, breakdown, and holding costs.
Abstract
This paper investigates the steady‐state performance of an queueing system subject to random and time‐homogeneous partial and complete server breakdowns. Under partial breakdown conditions, the server continues to provide service at a reduced rate, while service is entirely suspended during complete breakdown periods. By applying the Probability Generating Function (PGF) methodology, the joint probability distribution of the server state and the number of customers in the system is obtained. Several key performance measures are derived and numerically illustrated to highlight the influence of system parameters on overall performance. In addition, a structured cost model is developed to account for service, breakdown, and holding costs. A Genetic Algorithm (GA) is then employed to optimize the cost function and identify effective operational strategies for handling partial and complete breakdowns.
This paper investigates a single-server time-sharing queueing system with server breakdowns, discouraging arrivals and customer reneging. Customers arrive according to a Poisson process with rate λ while the server is operational. During server breakdowns, the arrival rate is reduced to represent customer discouragemen...
Priyanka Kapoor, S. Singh, Poonam· International Journal For Mu...· 0 citations
A heterogeneous two-server queueing system with differentiated vacations and server failures is examined in this paper. The matrix geometric method was applied to identify the system's stationary condition by analyzing the steady-state probability distribution of customer numbers, modeled as a quasi-birth-and-death (QB...
K. V, R. A., J. A et al.· Mathematics in Applied Scien...· 0 citations
The objective of this research is to investigate a novel retrial G-queue with one server. The concepts of preemptive priority, partial breakdown (working breakdown), feedback, and semi-active vacation (working vacation) are taken into consideration. There are two categories of consumers, which include priority consumer...
Nisha, Shweta Upadhyaya, Divya Agarwal et al.· WSEAS Transactions on Mathem...· 0 citations
We consider the dynamic scheduling problem in a multi-class M/G/N + M queue with convex delay costs and impatient customers that have exponential abandonment times. We apply the Whittle index approach to find a reasonable heuristic solution for this tricky problem. By assuming exponential abandonment times, we are able...
- This paper presents a comprehensive modelling and performance analysis of telecommunication queuing systems using Continuous-Time Markov Chains (CTMCs). The research addresses the stochastic nature of packet arrivals and service processes by developing mathematical representations for classic queuing models: M/M/1, M...
Owoade Praise Oluwapelumi, Ini Adinya, Folorunso Tobi Emmanuel· Iconic research and engineer...· 0 citations
In this paper, the Markovian model of queuing-inventory system with finite waiting room and catastrophes is considered. As a result of the catastrophes, all stocks in the warehouse are destroyed instantly. In addition to consumer customers, the system also takes into account customers who do not require service or inve...
A. Melikov, L. Poladova· Kibernetyka ta Systemnyi Ana...· 0 citations
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