STEADY-STATE AND FIRST PASSAGE TIME DISTRIBUTIONSFOR WAITING TIMES IN THE MAP/M/s + G QUEUEING MODEL WITH GENERALLY DISTRIBUTED PATIENCE TIMES

• Main Authors: Akar, N. (Author), Gursoy, O. (Author), Mehr, K.A (Author)
• Format: Article
• Language: English
• Published: American Institute of Mathematical Sciences 2022
• Subjects: Call center models; First passage time distribution; Generally distributed patience times; Markov fluid queues; Steady-state solution
• Online Access: View Fulltext in Publisher

 We study the MAP/M/s+G queueing model that arises in various multi-server engineering problems including telephone call centers, under the assumption of MAP (Markovian Arrival Process) arrivals, exponentially distributed service times, infinite waiting room, and generally distributed patience times. Using sample-path arguments, we propose to obtain the steady-state distribution of the virtual waiting time and subsequently the other relevant performance metrics of interest via the steady-state solution of a certain Continuous Feedback Fluid Queue (CFFQ). The proposed method is exact when the patience time is a discrete random variable and is asymptotically exact when it is continuous/hybrid, for which case discretization of the patience time distribution is required giving rise to a computational complexity depending linearly on the number of discretization levels. Additionally, a novel method is proposed to accurately obtain the first passage time distributions for the virtual and actual waiting times again using CFFQs while approximating the deterministic time horizons by Erlang distributions or more efficient Concentrated Matrix Exponential (CME) distributions. Numerical results are presented to validate the effectiveness of the proposed numerical method. © 2022. Journal of Industrial and Management Optimization. All Rights Reserved.