A Stochastic Model for Automated Teller Machines Subject to Catastrophic Failuresand Repairs

Abstract

In this paper we develop a queueing model useful in service industries dealing with Abstract: In this paper we develop a queueing model useful in service industries dealing withautomatic teller machines (ATMs) that are commonly used by people all over the world. We assume that automatic teller machines (ATMs) that are commonly used by people all over the world. We assume that these service systems are subject to failures due to catastrophic events such as power outage, mechanical these service systems are subject to failures due to catastrophic events such as power outage, mechanical or electrical problems. Arrivals of customers are modeled using a Markovian arrival process and the or electrical problems. Arrivals of customers are modeled using a Markovian arrival process and the service times are assumed to be of phase type. Individual customer cash requirements are modeled using service times are assumed to be of phase type. Individual customer cash requirements are modeled using a probabilistic rule and the machine has a finite capacity for holding the cash. Assuming the failure a probabilistic rule and the machine has a finite capacity for holding the cash. Assuming the failure times, repair times, and cash replenishment times to be exponential, we analyze the model using matrix- times, repair times, and cash replenishment times to be exponential, we analyze the model using matrix-analytic methods, and present two illustrative examples to bring out the salient features. Some well- analytic methods, and present two illustrative examples to bring out the salient features. Some well-known queueing-inventory models are shown to be special cases and in some of these cases we derive known queueing-inventory models are shown to be special cases and in some of these cases we derive explicit expressions for the steady-state probability vectors. The model studied is generic in that it can explicit expressions for the steady-state probability vectors. The model studied is generic in that it can be applied in the context of queueing-inventory situations.