Multiphase Queuing System of Blocking Queues and a Single Common Orbit Retrial Queue with Limited Buffer

We consider a multiphase queuing system of type M/M/1/k \(\rightarrow \) \(\bullet \) /M/1/k \(\rightarrow \) \(\cdots \) \(\rightarrow \) \(\bullet \) /M/1/k with an arbitrary number of nodes and a common retrial queue of type \(\bullet \) /M/1/k for other queues in the system. This kind of queuing system can serve as a model for wireless networks of asymmetric nodes, where a node with weak processing power can act as a temporary waiting place for blocked packets. An analytical model of the system is investigated and various performance measures of the system are derived. Comparisons of numerical results from the analytical model with simulation results are also performed. We then utilize the simulation model to explore the impact of the orbit node on system performance. Simulation results point out that in the situation of network saturation, the existence of the orbit queue brings little improvement to the performance of the system. On the other hand, in the case of near-saturation network and the case of low-utilization network with queues of small buffer size, the orbit node can improve the packet loss rate significantly, with the trade-off of increasing average response time.