Queueing systems in which blocked customers may retry for service after a random amount of time are called retrial queues. Retrial queues are useful in modeling many problems in telephone switching systems, telecommunication networks, computer networks and computer systems.
The main purpose of this thesis is to find the distribution of queue length for several variants of retrial queueing system.
In chapter 3, we consider an M/M/1 feedback retrial queue with geometric loss. As a feedback, after the customer is served, he will decide either to leave the system forever with probability 1-β or to join the retrial group again with probability β for another service. The joint distribution of the server state and queue length is derived by solving the confluent hypergeometric equation. We present some numerical examples on the mean queue length in the retrial group as feedback probability β varies.
In chapter 4, we consider an M/G/1 retrial queueing system with two types of priority customers and non-priority customers. In the case of blocking, the priority customers can be queued whereas the non-priority customers must join the retrial group in order to seek service again after a random amount of time. A priority customer who has received service departs the system with probability $1-\delta_1$ or return to the priority queue for more service with probability $\delta_1$. A non-priority customer who has received service leaves the system with probability $1-\delta_2$ or rejoins the retrial group with probability $\delta_2$. The joint generating function of the number of customers in two groups is derived by using the supplementary variable method. It is shown that our results are consistent with those already known in the literature when $\delta_k$ = 0(k =1,2),$\lambda_1 = 0$ or $\lambda_2 = 0$.
In chapter 5, we consider an M/M/2 retrial queue with geometric loss. The joint probabilities of the queue length and busy servers in the steady-state are derived by the method of series solution. Some numerical examples show that mean queue length for M/M/2 retrial queue with geometric loss increases as the service rate decreases and the probability of returning to retrial group after attempt's failure increases.
In chapter 6, we consider an $E_2$/M/1 retrial queue in which customers arrive according the general Erlangian distibution $E_2$. The joint generating function of the channel state, the arrival stage and the queue length is derived by solving the hypergeometric differential equation.