Equilibrium in a finite capacity M/M/1 queue with unknown service rates consisting of strategic and non-strategic customers

S. Srivatsa Srinivas () and Rahul R. Marathe ()
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S. Srivatsa Srinivas: Indian Institute of Technology Madras
Rahul R. Marathe: Indian Institute of Technology Madras

Queueing Systems: Theory and Applications, 2020, vol. 96, issue 3, No 6, 329-356

Abstract: Abstract We consider an $$M/M/1/{\overline{N}}$$ M / M / 1 / N ¯ observable non-customer-intensive service queueing system with unknown service rates consisting of strategic impatient customers who make balking decisions and non-strategic patient customers who do not make any decision. In the queueing game amongst the impatient customers, we show that there exists at least one pure threshold strategy equilibrium in the presence of patient customers. As multiple pure threshold strategy equilibria exist in certain cases, we consider the minimal pure threshold strategy equilibrium in our sensitivity analysis. We find that the likelihood ratio of a fast server to a slow server in an empty queue is monotonically decreasing in the proportion of impatient customers and monotonically increasing in the waiting area capacity. Further, we find that the minimal pure threshold strategy equilibrium is non-increasing in the proportion of impatient customers and non-decreasing in the waiting area capacity. We also show that at least one pure threshold strategy equilibrium exists when the waiting area capacity is infinite.

Keywords: Queueing game; Service operations; Strategic behavior; Threshold strategy equilibrium; 60K25; 90B22; 91A40 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11134-020-09671-x

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