Queueing Models and Service Management

The Non-parametric Asymmetric Kernel Method in the Study of M/G/1 Queue with Optional Second Service

Sedda Hakmi — 2026-06-02

This paper proposes the non-parametric asymmetric kernel method in the study of M/G/1 queue with optional second service. In this model customers arriving following a Poisson process and all demand the first service, while only some of them demand the second
service with probability p. The service times are assumed to follow a general distribution. We introduce the modified Gamma (MG) kernel method considered as a good alternative to parametric approaches such as mixture models for approximating the service and re-service time densities. Some performance measures related to this system are illustrated through simulation studies.

Retrial Queue with Balking, Synchronous Working Vacation Interruption, and Non-preemptive Priority

Ming-Chin Chen — 2026-06-02

This paper deals with a multi-server priority retrial queue with vacation interruption, where the servers are not completely out of service during the vacation period. The system serves two customers classes, denoted P₁ and P₂ . In the discussed system, there is no waiting space for class P₁ customers. Upon a class P₁ customer arrival epoch and all servers are occupied, the customer departs the system. On the other hand, upon a class P₂ customer arrival epoch and all servers are busy, he may balk the system or join the orbit. Whenever there are no customers in the system at the moment of service completion, all servers will be on vacation at the same time. After the vacation ends, the servers are reactivated only if at least q customers are found on the orbit; otherwise, the servers continue with another vacation. The vacation will be interrupted if there are more than or equal to q customers in orbit after the low-rate service is completed. For this system, the effect of system parameters on system characteristics is numerically illustrated. Finally, the optimization analysis is investigated to determine the optimal vacation rate and the optimal number of special servers to maximize profit.

On a Computational Method for Two Asymmetric Parallel Queues

Tayeb Lardjane — 2026-06-02

This paper addresses a well-known problem in queuing theory: the asymmetric shortest queue problem. The system consists of two parallel queues fed by a common Poisson arrival stream with rate λ. Upon arrival, each customer joins the shortest queue and
remains there until being served. If the two queues have the same length, the arriving customer chooses the queue 1 with probability α and the queue 2 with probability 1−α. Service times are exponentially distributed, with rate μ₁ for the queue 1 and rate μ₂ for the queue 2. No jockeying is permitted between the two queues. An easy and efficient method is presented for computing the steady state solution of the system.