Rational abnadomnets from an M/G/1 queue

Yoav Kerner, Ben Gurion University of the Negev

We consider an M/G/1 queue in which the customers, while waiting in line, observe the dynamics of the queue, and may decide reneging it.

We show that the Nash equilibrium profile is defined by two sequences of thresholds. 

For each customer, the decision is based on the observed past (that determines from what sequence the threshold is taken) and the observed queue length (that determines which element in the chosen sequence). 

We construct the set of equations that its solution is the Nash equilibrium and discuss the relation between the properties of the service time distribution and the properties of the Nash equilibrium (e.g. uniqueness, finiteness). 

Joint work with Eliran Schertzer