A Double-ended Queue with Catastrophes and Repairs, and a Jump-diffusion Approximation

Antonio Crescenzo (), Virginia Giorno (), Balasubramanian Krishna Kumar () and Amelia G. Nobile ()
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Antonio Crescenzo: Università di Salerno
Virginia Giorno: Università di Salerno
Balasubramanian Krishna Kumar: Anna University
Amelia G. Nobile: Università di Salerno

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 4, 937-954

Abstract: Abstract Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero. We study both the transient and steady-state probability laws of the stochastic process that describes the state of the system. We then derive a heavy-traffic approximation to the model that yields a jump-diffusion process. The latter is equivalent to a Wiener process subject to randomly occurring jumps, whose probability law is obtained. The goodness of the approximation is finally discussed.

Keywords: Bilateral birth-death processes; Double-ended queues; Transient probabilities; Catastrophes; Disasters; Repairs; Continuous approximations; Jump-diffusion processes; Transition densities; Primary 60J80; Secondary 60J25 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (13)

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DOI: 10.1007/s11009-011-9214-2

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