Non-cooperative queueing games on a network of single server queues

Non-cooperative queueing games on a network of single server queues

Laan, C.M.
Timmer, J.
Boucherie, R.J.

2021

This paper introduces non-cooperative games on a network of single server queues with fixed routes.Aplayer has a set of routes available and has to decide which route(s) to use for its customers. Each player’s goal is to minimize the expected sojourn time of its customers. We consider two cases: a continuous strategy space, where each player is allowed to divide its customers over multiple routes, and a discrete strategy space, where each player selects a single route for all its customers. For the continuous strategy space, we show that a unique pure-strategy Nash equilibrium exists that can be found using a best-response algorithm. For the discrete strategy space, we show that the game has a Nash equilibrium in mixed strategies, but need not have a purestrategy Nash equilibrium. We show the existence of pure-strategy Nash equilibria for four subclasses: (i) N-player games with equal arrival rates for the players, (ii) 2-player games with identical service rates for all nodes, (iii) 2-player games on a 2 × 2-grid, and (iv) 2-player games on an A × B-grid with small differences in the service rates.

Routing
Network of single-server queues
Non-cooperative games ·
Pure-strategy Nash equilibrium
Defence, Safety and Security

http://resolver.tudelft.nl/uuid:d4b67ab6-b2c8-496f-9338-ae4109b7ba5c

946811

MO

Queueing Systems

open access

article