Condition-Based Maintenance for Queues With Degrading Servers

Abstract

The integration of condition monitoring with queueing systems to support decision making is not well explored. This work addresses the impact of condition monitoring of the server on the system level performance experienced by entities in a queueing system. The system consists of a queue with a single server subject to Markovian degradation. The model assumes a Poisson arrival process with service times and repair times according to general distributions. We develop stability conditions and perform steady state analysis to obtain performance measures (average queue length, average degradation, etc.). We propose minimizing an objective function involving four types of costs: repair, catastrophic failure, quality and holding. The queue performance measures derived from steady state analysis are bench-marked and compared to those from a discrete event simulation model. After verifying the queuing model, a sensitivity analysis is performed to determine the relationships between system performance and model parameters. Further, we explore the impact of stochastic service times on degradation and cost coefficients on optimal repair policy.Results indicate that the total cost function is convex and thus subject to an optimal repair policy.The model is sensitive to service time, quality costs, and failure costs for late-stage policy repairs decisions and sensitive to expected repair times and repair costs for early-stage policy repair decisions. The stochastic nature of service times drastically increases the likelihood of catastrophic failure of the server, and substantially increases holding costs. However, quality degrades more for constant service times while repair costs are minimally impacted.

Analysis of MAP/PH/1 Queueing System with Degrading Service Rate and Phase Type Vacation

“…Note that A 0 , A 1 , and A 2 are square matrices of order Lmn. The dimensions of the other matrices appearing in Q (1) should be self-explanatory.…”

“…Assuming that the stability condition given in Equation ( 1) holds good, the steadystate probability vector of Q (1) exists. Let x = (x 0 , x 1 , • • • ) be the steady-state probability vector such that…”

“…Then, due to the nature of Q (1) , which is a QBD− process, the steady-state probabilities are (see in [31]) obtained as…”

“…Machines are the integral part of industrial systems as well as in our daily life. To address the issue of degrading service maintenance, strategies are required, and a condition-based maintenance for a single-server queueing system is analyzed by Ejaz et al [1]. Due to the nature of offering continuous services to customers, one could expect some form of degradation to the service provided.…”

“…Due to the nature of offering continuous services to customers, one could expect some form of degradation to the service provided. While degradation is addressed in the context of (condition-based) maintenance in the literature (see in [1]) to the best of our knowledge the degradation of services in the context of a more general queueing model has not been addressed so far. queueing models play an important role in the study of service systems.…”