Abstract
Queueing models with disasters can be used to evaluate the impact of a breakdown or a system reset in a service facility. In this paper, we consider a discrete-time single-server queueing system with general independent arrivals and general independent service times and we study the effect of the occurrence of disasters on the queueing behavior. Disasters occur independently from time slot to time slot according to a Bernoulli process and result in the simultaneous removal of all customers from the queueing system. General probability distributions are allowed for both the number of customer arrivals during a slot and the length of the service time of a customer (expressed in slots). Using a two-dimensional Markovian state description of the system, we obtain expressions for the probability, generating functions, the mean values, variances and tail probabilities of both the system content and the sojourn time of an arbitrary customer under a first-come-first-served policy. The customer loss probability due to a disaster occurrence is derived as well. Some numerical illustrations are given.
Highlights
Queueing models with negative arrivals have been studied extensively over the last decades, owing to their applicability in the performance analysis of a wide range of systems, such as computers, telecommunication systems and manufacturing systems
Our current work further extends the existing results in the literature to a discrete-time disaster model, where general probability distributions are allowed for both the number of customer arrivals during a slot and the length of a customer service time
We present a full queueing analysis of this queueing model with disasters and derive expressions for the probability generating functions as well as the mean values, variances and tail probabilities of both the system content and the sojourn time under a first-come-firstserved (FCFS) policy
Summary
Queueing models with negative arrivals have been studied extensively over the last decades, owing to their applicability in the performance analysis of a wide range of systems, such as computers, telecommunication systems and manufacturing systems. The first study [3] on discrete-time queues with disasters considered the Geo/Geo/1 queueing model with a Bernoulli distribution of the number of customer arrivals per slot and geometric service times under the impact of Bernoulli disasters. The extension to a discrete-time Geo/G/1 disaster model with Bernoulli arrivals and general independent service times was considered in [6] (system content) and [7,8] (sojourn time). Our current work further extends the existing results in the literature to a discrete-time disaster model, where general probability distributions are allowed for both the number of customer arrivals during a slot and the length of a customer service time.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
