Network of fuzzy queues: a shortest path

Vast applications of network of queues made it one of the most important issues in the queuing theory. Due to this importance a novel network of queues which meets more real world conditions will be discussed. This paper describes a network of queues constructed from fuzzy interarrival and service times. Fuzzy arcs with triangular fuzzy lengths, times, connect these queues. To find a single source-single destination shortest path in this network, a two step transformation was needed. First step transforms the fuzzy queuing system to fuzzy triangular waiting time. Based on the results of the first step, the nodes of the network are transformed to corresponding fuzzified arcs. A hybrid algorithm combining a fuzzy simulation and a genetic algorithm is utilized to find the shortest path on this network of queues. Experimental results showed that the algorithm converges by a good rate. The maximum relative error observed for a complicated cyclic network is 0.8%.

Keywords:

Fuzzy network of queues , Fuzzy simulation , Genetic algorithm , Shortest path