We consider the processor sharing M/M/1-PS queue which also models balking. A customer that arrives and sees n others in the system “balks” (i.e., decides not to enter) with probability 1 − bn. If bn is inversely proportional to n + 1, we obtain explicit expressions for a tagged customer’s sojourn time distribution. We consider both the conditional distribution, conditioned on the number of oth...

This paper considers a nonstationary multiserver queuing model with abandonment and balking for inbound call centers. We present a continuous time Markov chain (CTMC) model which captures the important characteristics of an inbound call center and obtain a numerical solution for its transient state probabilities using uniformization method with steady-state detection.

The aim of this paper is to treat the analytical solution of the truncated interarrival hyperexponential machine interference queue: H2/M/1/m+Y/m+Y in case of two branches with the following concepts: balking, reneging, state-dependent, spares, and an additional server for longer queues. Our research treats the general case for the values of m and Y considering the discipline FIFO. And some spe...

This paper deals with the optimal control policy of two-phase service M X / Ek /1 queues with vacation, N-policy, server break downs and balking. Generating functions method is used to derive the system characteristics. The total expected cost function is developed to determine the optimal threshold of N at a minimum cost. Numerical experiment is performed to validate the analytical results. Th...

We consider a Markovian queue subject to Poisson generated catastrophes. Whenever a catastrophe occurs, all customers are forced to abandon the system, the server is rendered inoperative and an exponential repair time is set on. We assume that the arriving customers decide whether to join the system or balk, based on a natural reward-cost structure. We study the balking behavior of the customer...

We consider a Markovian queue subject to Poisson generated catastrophes. Whenever a catastrophe occurs, all customers are forced to abandon the system, the server is rendered inoperative and an exponential repair time is set on. We assume that the arriving customers decide whether to join the system or balk, based on a natural reward-cost structure. We study the balking behavior of the customer...

In a G/GI/c loss system with balking, reneging, or limited waiting space, deleting some of the arriving customers can either increase or decrease the fraction of the remaining arrivals who get served, depending on how customers are deleted. We present a model in which the random deletion of arrivals independently and with some fixed probability can never decrease the fraction of the remaining a...