A discrete time single-server queue with balking: economic applications

Abstract

This article studies a discrete time single-server queue with finite and infinite buffer where the users have the option to leave the queue upon arrival (balking). We consider two variants of the model in accordance with the balking policies. Firstly, all the arriving customers balk with a constant probability. Secondly, arriving customers increase their balking probabilities as more customers join the system. Specifically, we find the ergodicity condition and closed-form expressions for the stationary distribution of the system size, of the waiting/spending time in the FCFS system and of the unfinished work. The mathematical model is applied in order to resolve several real-life problems in the economic field; in this sense, practical applications in the secondary and tertiary sector are shown. We also develop a cost model to determine the buffer capacity that minimizes certain cost function and give some numerical examples.

Analysis of Discrete-Time Single Server Queue with Balking and Multiple Working Vacations

“…K , that is the server never takes any vacation. The model reduces to 1 N Geo Geo queue with balking and our results match analytically with the results posed in Lozano and Moreno [13]. .…”

Optimising the booking horizon in healthcare clinics considering no-shows and cancellations

“…For example, the service time in appointment systems starts on predefined timeslots, impacting the utilisation in case of empty appointment slots. This discretetime nature of the appointment slots could be included in the queueing model to better capture the relationship between the booking horizon and scheduling interval (Creemers and Lambrecht 2010;Meisling 1958;Hernández-Díaz and Moreno 2009;Lozano and Moreno 2008).…”

Discrete-time renewal input queue with balking and multiple working vacations

“…Customers' impatience in a GI/M/1/N queue with WV has been studied by Goswami (2014b) using supplementary variable and recursive techniques. Closed form expressions for the stationary system size distributions of a discrete-time single server queue with balking have been obtained by Lozano and Moreno (2008). Liu and Gao (2010) studied the discrete-time Erlang loss system with server breakdowns in which the customer being served before server breakdown decides to depart the system with a certain probability.…”