Comparative and performance analyses of unreliable server queues

Abstract

Queue-based scenarios with server breakdowns have become an exciting topic for queueing theorists, researchers, and practitioners in past decades. These queueing systems are generally used in many realistic waiting line models in our day-to-day life, such as computer and communication systems, production systems, transportation systems, flexible manufacturing systems, etc. Several scholars and researchers have worked on queueing systems with server breakdowns and provided significant results during the last few decades. Gaver [1] and Shogan [2] investigated queueing systems with server breakdowns and provided explicit expressions of several queuing-based system performance indicators. Jayaraman et al. [3] studied a bulk queueing system with state-dependent arrival rate and server breakdown. In 2004, Ke [4] discussed a bi-level control policy for the batch arrival queue with an early start-up and unreliable server. Later, Jain and Agrawal [5] considered an https://www.w3.org/1998/Math/MathML" display="inline"> M X / M /1 https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003481263/3627ff2f-b685-486a-bdfb-379751e6ddcc/content/inline-math8_1.tif"/> queueing system with multiple breakdown states of the unreliable server under https://www.w3.org/1998/Math/MathML" display="inline"> N https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003481263/3627ff2f-b685-486a-bdfb-379751e6ddcc/content/inline-math8_2.tif"/> -policy. In the same year, Wang and Yang [6] investigated a controllable queueing system with an unreliable server. They illustrated many interesting numerical experiments for the optimal analysis using the semi-classical optimizer, the Quasi-Newton method. For more in-depth analysis, one can refer to the research findings in (cf. [7–15]) and references therein. Recently, Ke et al. [16] studied a feedback retrial queue with balking behavior of the customer and unreliable server and developed a cost optimization problem determining the optimal parameter setting under the stability condition using Probability Global Search Lausanne (PGSL) approach. A retrial queueing system with a finite number of sources and customers collision is discussed by Nazarov et al. [17]. They proved that the limiting probability distribution of the number of customers in the queueing system follows a Gaussian distribution.