Pooling in tandem queueing networks with non-collaborative servers

• Published in: Queueing systems Vol. 87; no. 3-4; pp. 345 - 377
• Main Authors: Argon, Nilay Tanık, Andradóttir, Sigrún
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2017; Springer Nature B.V
• Subjects: Buffers; Business and Management; Computer Communication Networks; Control; Markov analysis; Operations Research/Decision Theory; Probability Theory and Stochastic Processes; Queues; Queuing theory; Servers; Stations; Supply Chain Management; Systems Theory; Sample-path analysis; 90B22; Stochastic orders; Production blocking; Tandem queues; Throughput; Finite buffers; Work-in-process inventory (WIP); 60K25
• ISSN: 0257-0130; 1572-9443
• DOI: 10.1007/s11134-017-9543-0

This paper considers pooling several adjacent stations in a tandem network of single-server stations with finite buffers. When stations are pooled, we assume that the tasks at those stations are pooled but the servers are not. More specifically, each server at the pooled station picks a job from the incoming buffer of the pooled station and conducts all tasks required for that job at the pooled station before that job is placed in the outgoing buffer. For such a system, we provide sufficient conditions on the buffer capacities and service times under which pooling increases the system throughput by means of sample-path comparisons. Our numerical results suggest that pooling in a tandem line generally improves the system throughput—substantially in many cases. Finally, our analytical and numerical results suggest that pooling servers in addition to tasks results in even larger throughput when service rates are additive and the two systems have the same total number of storage spaces.