Upper and lower bounds for the waiting time in the symmetric shortest queue system
The classical shortest queue model with two servers is considered. To evaluate performance of the system numerically with error bounds the authors introduce two auxiliary models: the shortest queue system with threshold jockeying and the shortest queue system with threshold blocking. In the system with threshold jockeying one customer moves from the longest queue to the shortest queue as soon as the difference between these queues exceeds a certain threshold. In the system with threshold blocking the server in the shortest queue is switched of as soon as the difference between these queues reaches a certain threshold. The main result of the paper states that the total number of customers in the original system is stochastically less (greater) than the total number of customers in the system with threshold blocking (jockeying). Since the auxiliary systems can be effectively analyzed numerically with the help of matrix-geometric technique due to M. Neuts, this allows calculation of performance characteristics of the original system.
scientific article; zbMATH DE number 513135
scientific article