PHASE 2:

Abstract

A Jackson Queuing Network (JQN) [2] is a system consisting of a number of n interconnected queuing stations. A JQN with two queues is depicted in Figure 1 Jobs arrive from the environment with a negative exponential inter-arrival time and are distributed to station i with probability r 0,i. Each station is connected to a single server which handles the jobs with a service time given by a negative exponential distribution with rate µ i. Jobs processed by the station of queue i leave the system with probability r i,0 but are put back into queue j with probability r i,j. JQNs have an infinite state-space because the queues are unbounded. Initially all queues are empty. In this test case we consider JQN models with N = 3, 4, 5 queues. The arrival rate for N queues is λ, which is then distributed to station j (with service rate µ j = j) with probability 1 µ j · N i=1 µ i The probability out of a service rate is then uniformly distributed. We compute the probability that, within t = 10 time units, a state is reached in which 4 or more jobs are in the first and 6 or more jobs are in the second queue.