Strategic behaviour in a tandem queue with alternating server

Nimrod Dvir (), Refael Hassin () and Uri Yechiali ()
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Nimrod Dvir: Tel-Aviv University
Refael Hassin: Tel-Aviv University
Uri Yechiali: Tel-Aviv University

Queueing Systems: Theory and Applications, 2020, vol. 96, issue 3, No 2, 205-244

Abstract: Abstract This paper considers an unobservable two-site tandem queueing system attended by an alternating server. We study the strategic customer behaviour under two threshold-based operating policies, applied by a profit-maximizing server, while customers’ strategic behaviour and server’s switching costs are taken into account. Under the Exact-N policy, in each cycle the server first completes service of N customers in the first stage ( $$Q_1$$ Q 1 ), then switches to the second stage ( $$Q_2$$ Q 2 ) and then serves those N customers before switching back to $$Q_1$$ Q 1 to start a new cycle. This policy leads to a mixture of Follow-the-Crowd and Avoid-the-Crowd customer behaviour. In contrast, under the N-Limited policy, the server switches from $$Q_1$$ Q 1 to $$Q_2$$ Q 2 also when the first queue is emptied, making this regime work-conserving and leading only to Avoid-the-Crowd behaviour. Performance measures are obtained using matrix geometric methods for both policies and any threshold N, while for sequential service ( $$N=1$$ N = 1 ) explicit expressions are derived. It is shown that the system’s stability condition is independent of N, and of the switching policy. Optimal performances in equilibrium, under each of these switching policies, are analysed and compared through a numerical study.

Keywords: Strategic behaviour; Tandem queues; Alternating server; Threshold policy; Switching cost; Equilibrium; Follow-the-Crowd; Avoid-the-Crowd; 60K25; 60K30; 90B22; 91A10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11134-020-09665-9

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