This investigation deals with single server queueing system wherein the arrival of the units follow Poisson process with varying arrival rates in different states and the service time of the units is arbitrary (general) distributed. The server may take a vacation of a fixed duration or may continue to be available in the system for next service. Using the probability argument, we construct the set of steady state equations by introducing the supplementary variable corresponding to elapsed service time. Then, we obtain the probability generating function of the units present in the system. Various performance indices, such as expected number of units in the queue and in the system, average waiting time, etc., are obtained explicitly.Some special cases are also deduced by setting the appropriate parameter values. The numerical illustrations are provided to carry out the sensitivity analysis in order to explore the effect of different parameters on the system performance measures.

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.

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.

In this article‎, ‎the Bayesian estimation of the traffic intensity parameter for the M/M/1 queuing system is performed when it follows a beta prior distribution‎. ‎The analysis is conducted under the general entropy and linear exponential loss functions‎, ‎considering a Type II censoring scheme based on fuzzy data‎. ‎Furthermore‎, ‎the obtained estimators compared under these two loss functions using an extensive Monte Carlo simulation study‎. ‎A real-world data set is also utilized to determine the more appropriate estimator.