Researches Of Queueing Model In Communication Networks

Communication networks have made significant progress with technological advances in the recent years. But higher network throughput, wider network coverage, larger number of users, and better network quality will be demanded in the future communication networks. To satisfy these requirements, we construct two types'useful queueing models to provide performance measures of communication networks to maximize the utilization of resources.The type I model, which have many queueing polices, is the one that the inter-arrival time or service time is exponential distribution based on the requirements of analytical solution.Firstly, an M/G/1 non-preemptive priority with general retrial times and server subject to breakdowns and repairs is considered. Using a supplementary variable method, we derived the ergodicity of the embedded Markov chain, its stationary distribution function and the joint generating function of the number of calls in both groups in the steady-state regime. Some main reliability indexes, such as availability, failure frequency, and the reliability function of the server are also obtained. Besides, we give numerical examples to illustrate the effect of parameters on several performance characteristics.Secondly, we consider the model which is the multi-server queueing model that arrival rate and service rate of customers vary randomly according to changes of the random environment; customers can be lost because of the network environment. Using quasi-birth-death (QBD) process, we obtain the necessary and sufficient condition for the stability of system, the conditional indexes and overall means of the queue in every state are obtained Additionally, The effect of system parameters on the system performance measures is discussed, the affect of various parameters of Rush-hour on the system state and busy cycle are illustrated numerically.Then we construct the MAP/M/(c/∞) Queue with Markovian Flow of Breakdowns, This model is quite general enough to cover most of the communication networks. The necessary and sufficient condition for the system stability is obtained, and the queue and main indexes reliability of servers are also derived by a quasi-birth-and-death process. Besides, we give numerical examples to compare the effect of different input flows to the queueing performance characteristics.The typeⅡmodel, with the characteristics of wireless cellular network, is the one that the inter-arrival time and service time are (batch) Markov Arrival Process (MAP) and Phase-type (PH) distribution. The conclusions of model give many performance measures of the communication networks, which can provide the useful ways with the performance analysis and optimization of cost-benefit.In the first place, we construct the model, there are finite positions in the buffer of wireless cellular networks, which handoff and new calls have different arrival rate of Markov arrival processes, and their service time distributions are different Phase-type distributions. Using matrix analytic techniques, we obtain the blocking probability of new calls and the dropping probability of handoff calls, the meaning waiting time and the mean queue lengths of two types of calls. We give numerical results to show input of different calls arrival rate on performance measures. Besides, we study the effect of the service rate of customer on expected total cost.In the second place, we relax exponential inter-arrival assumption by using Markov arrival process and Phase-type distribution of service times. For channel allocation, guard channels are reserved for handoff calls to decrease the loss of handoff ones. Using matrix analytic techniques, we obtain the blocking probability of new calls and the dropping probability of hand off calls, the meaning waiting time and the mean queue lengths of two types of calls. We give numerical results to show input of different calls arrival rate on performance measures. Besides, the way of calculating expected total cost is given.In the end, we consider the retrial queue with finite-position buffer which handoff and new calls have different arrival rate of Batch Markov Arrival Process (BMAP). The behavior of system is described in terms of continuous time multi-dimensional Markov chain. The server can provide two types heterogeneous services with Phase-type time distribution to each arriving call. Arriving calls have an option to choose either type of services. This model is quite general enough to cover most of the systems in communications networks. We derive the ergodicity condition and calculate the stationary distribution and the main performance characteristic of the system. The effects of various parameters on the system performance measures are illustrated numerically.