Mean queue time study for the Lu-Kumar network

Manufacturing system, communication network, silicon wafer manufacturing plant, internet service provider domain and freeway system are usually modelled with multi-class queuing network. The aim of this project is to deeply understand the nature of the Lu-Kumar network. The queue time of the Lu-Kumar network is hard to predict due to the mutual blocking of virtual stations in the network. In most of the literature, the stability of a network is discussed using a fluid model. But in this project, the stability of a network is investigated by mean of manual book-keeping as well as simulation model with deterministic inter-arrival time and service time. The condition, for which the network will come back to the stable state when there is a small disturbance at an initial state, is also examined. To understand the nature of virtual stations in a network, the network is simulated with MatEvent simulation model in which Poisson distribution is used for inter-arrival time and Exponential distribution is used for service times. Moreover, two buffers at service centre B of the Lu-Kumar network are merged into one queue to understand the blocking nature of the network and the queue time is compared with MM1 queue time. From the book-keeping and simulation result, it is found that the stability region of the deterministic Lu-Kumar network is discrete. It is about 1.5 times of more consecutive jobs are needed for the system started with double 0.9 inter-arrival time than that started with single 0.9 inter-arrival time. Furthermore, total queue time of the network with exponential distribution arrival time and service time shows strong linearity relationship with MM1 queue time. Thus, the queue time of the Lu-Kumar network can be approximated by Kingman’s approximation if the coefficient of variability can be determined. It is also recommended to find out the coefficient of variability in the network analytically. When two buffers at service centre B are merged into one queue, it shows the similar behaviour of MM1 model at two extreme points. In this project, the network is started with either single or double 0.9 inter-arrival times and the threshold for each system to come back to the stable state is determined. It is recommend to examine the critical point for the network started with triple 0.9 inter-arrival time to come back to the stable state and compare with two cases explained in this report.Bachelor of Engineering (Mechanical Engineering