We consider the virtual queueing time (vqt, also known as work-in-system, or virtual-delay) process in an M/G/s queue with impatient customers. We focus on the vqt-based balking model and relate it to reneging behavior of impatient customers in terms of the steady-state distribution of the vqt process. We construct a single-server system, analyze its operating characteristics, and use them to a...

In the present investigation transient, G x/G/m queuing model with balking and reneging has been studied. The diffusion process with elementary return boundary has been used for modeling purpose. The probability density function (p. d. f.) for the number of customers in the system has been obtained. In special case, the steady state results that tally with those of Kimura and Ohsone have been e...

This investigation deals with multi server queue with balking. The customers arrive in poisson fashion and independent of time, under the assumption that system is initially empty. The number of customers in the system is stochastically increasing and distributed in steady state (stationary state) as required. The expressions for the measure of the speed of convergence from transient state to s...

This paper presents stochastic modelling of a single server, finite buffer Markovian queuing system with discouraged arrivals, balking, reneging, and retention reneged customers. Markov process is used to derive the steady-state solution model. Closed form expressions using probability generating functions (PGFs) are derived presented for both classical novel performance measures. In addition, ...

Consider an Ornstein–Uhlenbeck process with reflection at the origin. Such a process arises as an approximating process both for queueing systems with reneging or state-dependent balking and for multiserver loss models. Consequently, it becomes important to understand its basic properties. In this paper, we show that both the steady-state and transient behavior of the reflected Ornstein–Uhlenbe...