STRATEGIC DYNAMIC JOCKEYING BETWEEN TWO PARALLEL QUEUES

• Published in: Probability in the engineering and informational sciences Vol. 30; no. 1; pp. 41 - 60
• Main Authors: Dehghanian, Amin, Kharoufeh, Jeffrey P., Modarres, Mohammad
• Format: Journal Article
• Language: English
• Published: New York, USA Cambridge University Press 01.01.2016
• Subjects: Arrivals; Dynamic programming; Dynamical systems; Dynamics; Optimization; Parallel processing; Policies; Queues; Queuing; Servers; Stations
• ISSN: 0269-9648; 1469-8951
• DOI: 10.1017/S0269964815000273

Consider a two-station, heterogeneous parallel queueing system in which each station operates as an independent M/M/1 queue with its own infinite-capacity buffer. The input to the system is a Poisson process that splits among the two stations according to a Bernoulli splitting mechanism. However, upon arrival, a strategic customer initially joins one of the queues selectively and decides at subsequent arrival and departure epochs whether to jockey (or switch queues) with the aim of reducing her own sojourn time. There is a holding cost per unit time, and jockeying incurs a fixed non-negative cost while placing the customer at the end of the other queue. We examine individually optimal joining and jockeying policies that minimize the strategic customer's total expected discounted (or undiscounted) costs over finite and infinite time horizons. The main results reveal that, if the strategic customer is in station 1 with ℓ customers in front of her, and q1 and q2 customers in stations 1 and 2, respectively (excluding herself), then the incentive to jockey increases as either ℓ increases or q2 decreases. Numerical examples reveal that it may not be optimal to join, and/or jockey to, the station with the shortest queue or the fastest server.