Profit maximization in flexible serial queueing networks

• Published in: Queueing systems Vol. 77; no. 4; pp. 427 - 464
• Main Authors: Kırkızlar, Eser, Andradóttir, Sigrún, Ayhan, Hayriye
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.08.2014; Springer Nature B.V
• Subjects: Buffers; Business and Management; Computer Communication Networks; Control; Costs; Dynamical systems; Employment; Nonlinear dynamics; Operations Research/Decision Theory; Policies; Probability Theory and Stochastic Processes; Quality; Quality of service; Queuing theory; Servers; Studies; Supply Chain Management; Systems Theory; Thresholds; 90B22; Buffer size optimization; 90C40; Flexible servers; Profit maximization; Queueing control; 60J28; Finite buffers; Holding cost
• ISSN: 0257-0130; 1572-9443
• DOI: 10.1007/s11134-014-9393-y

We analyze the tradeoff between efficiency and service quality in tandem systems with flexible servers and finite buffers. We reward efficiency by assuming that a revenue is earned each time a job is completed, and penalize poor service quality by incorporating positive holding costs. We study the dynamic assignment of servers to tasks with the objective of maximizing the long-run average profit. For systems of arbitrary size, structured service rates, and linear or nonlinear holding costs, we determine the server assignment policy that maximizes the profit. For systems with two stations, two servers with arbitrary service rates, and linear holding costs, we show that the optimal server assignment policy is of threshold type and determine the value of this threshold as a function of the revenue and holding cost. The threshold can be interpreted as the best possible buffer size, and hence our results prove the equivalence of addressing service quality via a holding cost and via limiting the buffer size. Furthermore, we identify the optimal buffer size when each buffer space comes at a cost. We provide numerical results that suggest that the optimal policy also has a threshold structure for nonlinear holding costs. Finally, for larger systems with arbitrary service rates, we propose effective server assignment heuristics.