Infinite divisibility and unimodality and their related concepts are important tools in distribution theory. They are of potential importance in both theory and applications. In this article, we shall utilize these properties to characterize some queuing systems such as M/G/oo amongst all GI/G/S/N queues and the systems M/M/1 and M/M/oo amongst M!M/S queues and reveal some related results. Our results generalize some findings of Haberland (1975), Shan hag (1973) and Laslett (1975) in this connection.

The Redundancy Allocation Problem (RAP) aims to optimize system reliability or cost by selecting redundant components under given constraints. While traditional RAP studies focus on reliability or cost alone, real-world systems, particularly Queueing networks, require a balance between redundancy allocation and operational performance. This paper investigates the RAP for a tandem Queueing network with repairable subsystems, where Queueing costs and repair costs are jointly minimized. Unlike prior works, our model integrates Queueing dynamics into redundancy optimization, ensuring both system reliability and operational efficiency. To solve this NP-hard problem, we propose a hybrid simulation-PSO algorithm, combining simulation for performance evaluation and Particle Swarm Optimization (PSO) for efficient solution search. Extensive numerical experiments demonstrate that our approach effectively minimizes total system costs while maintaining reliability. The results validate the applicability of our model in real-world service and manufacturing systems, such as healthcare, assembly lines, and logistics networks.

Control of the service process for the queuing system M/G/1 has been considered in [1] by the author, and the Lap lace transform of the length of the shut-down phase are obtained. In this paper we have evaluated the Lap lace transform of the length of busy period and the Lap lace transform of the queuing time distribution of an arbitrary customer for the (O,N,Q) control. Analysis of the sensitivity of the (O,N,Q) control parameters on the queuing time distribution is considered.

A two server Queueing System With Single and Batch Service is considered in this paper. The arrival process is assumed to be Poisson and the service rate follows an exponential distribution. Server-I serves the customers in both single and batch service, while server-II serves the customers in batch service only.  The Laplace transform of the transient and steady state behavior of the model is considered and we obtained the expressions for the expected queue length.

Since late 1960's, the emergency location problems, fire stations and medical emergency services have attracted the attention of researchers. Mathematical models, both deterministic and probabilistic, have been proposed and applied to find suitable locations for such facilities in many urban and rural areas. Here, we review some models proposed for finding the location of such facilities, with an eye on successfully implemented real life applications. We then propose an extension of the QM-CLAM model of Marianov and Serra (1998) to M/G/k systems, and suggest a GRASP type heuristic procedure for solving the problem. To improve the computed solution, local search heuristics are used. Sensitivity analysis and some computational results are also presented.

In this paper the control of the service process of an M/G/1 queuing system is considered. Whenever the server is behind the counter, he continues serving customers until the queue becomes empty. He then closes down the counter and returns only when either a queue exceeds a threshold level Q, where N is a positive integer and Q is a fixed positive value. Details on the probability density function of the number of customers and the Lap lace-transform of the length of the shut-sown phase are presented.