Discrete-time Sm Of [k] / Ph [k] / C (c = 1,2) / Fcfs Queue Queuing System Age

In this thesis,we study a discrete time queueing system with multiple types of customers and a first-come-first-served (FCFS)service discipline.Customers arrive according to a semi-Markov arrival process and the service times of individual customers have PH-distributions.In this thesis at first is the introduction,which introduces and analyses the study nowadays of discrete time queueing models with multiple types of customers.The first chapter gives an introduction about the knowledge of this thesis and calcula-tional methods.The second chapter describes SM[K]/PH[K]/1/FCFS queue and analyses its generalized age process particularly. We introduce some auxiliary variables to construct a Markov chain associated with α_g(t) and obtain the transition probability matrix of this Markov chain.The pivot of this thesis is the third chapter which at first describes SM[K]/PH[K]/2/FCFS queue and then analyses its generalized age process.We choose the age of some batch in queueing system as the age of this system skillfully to reduce the calculational complexity.We introduce some auxiliary variables to construct a Markov chain associated with α_g(t) and find the transition probability matrix of this Markov chain in detail.The fourth chapter analyses the steady state distribution of the age process of SM[K]/PH[K]/2/FCFS queue. Given the steady state distribution,we have pilot study of other information in a queueing system.