Behavior-Aware Queueing: The Finite-Buffer Setting with Many Strategic Servers
In “Behavior-Aware Queueing: The Finite-Buffer Setting with Many Strategic Servers,” Zhong, Gopalakrishnan, and Ward develop a game-theoretic many-server Markovian queueing model with finite or infinite buffers to study the behavior of strategic servers whose choice of work speed depends on manageri...
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Veröffentlicht in: | Operations research 2023-07 |
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Zusammenfassung: | In “Behavior-Aware Queueing: The Finite-Buffer Setting with Many Strategic Servers,” Zhong, Gopalakrishnan, and Ward develop a game-theoretic many-server Markovian queueing model with finite or infinite buffers to study the behavior of strategic servers whose choice of work speed depends on managerial decisions regarding (i) how many servers to staff and how much to pay them and (ii) whether and when to turn away customers. In order to predictably control system performance (e.g., lost demand, customer wait times, server burnout, etc.), they show that the system manager must either staff enough servers or pay them enough. For example, when servers are not paid enough, increasing their workload beyond a tipping point may result in a sharp drop in system performance because of server “rebellion.” Their work also establishes key foundational building blocks to advance the analysis of behavior-aware queueing models where both customers and servers are strategic and customers’ decisions endogenously induce a finite buffer.
Service system design is often informed by queueing theory. Traditional queueing theory assumes that servers work at constant speeds. That is reasonable in computer science and manufacturing contexts. However, servers in service systems are people, and in contrast to machines, the incentives created by design decisions influence their work speeds. We study how server work speed is affected by managerial decisions concerning (i) how many servers to staff and how much to pay them and (ii) whether and when to turn away customers in the context of many-server queues with finite or infinite buffers (
M
/
M
/
N
/
k
with
k
∈
Z
+
∪
{
∞
}
) in which the work speeds emerge as the solution to a noncooperative game. We show that a symmetric equilibrium always exists in a loss system (
N
=
k
) and provide conditions for equilibrium existence in a single-server system (
N
= 1). For the general
M
/
M
/
N
/
k
system, we provide a sufficient condition for the existence of a solution to the first-order condition and bounds on such a solution; however, showing that it is an equilibrium is challenging because of the existence of multiple local maxima in the utility function. Nevertheless, in an asymptotic regime in which demand becomes large, the utility function becomes concave, allowing us to characterize underloaded, critically loaded, and overloaded equilibria.
Funding:
This work was supported in part by funding from the Social Sciences and Humanities Resear |
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ISSN: | 0030-364X 1526-5463 |
DOI: | 10.1287/opre.2023.2487 |