Short run dynamics of multi-class queues
The paper studies the dynamics of general queueing systems with multiple classes of customers undergoing self-selection. The stability of arrival rates is of great importance in design of such systems, if the capacity is large enouth, the equilibrium arrival rate will be stable. Allowing the customer classes to have any smooth distribution for their service time and for the queue to have arbitrary delay function with some mild restrictions it is shown that if the capacity of the queue is too low then the system becomes unstable in a specific manner, in case of ``periodic-doubling bifurcation'' creating a stable periodic orbit nearby. Thus though the equilibrium arrival rate is unstable, the arrival rate always ends near the equilibrium and makes small oscillations about it.
scientific article; zbMATH DE number 550411
scientific article