Approximate analysis of open network of GE/GE/m/N queues with transfer blocking

In this paper we describe an approximate method for the analysis of an open network of finite capacity queues. Finite buffer capacities at the nodes introduce blocking of jobs that finish service at a node and find that the destination node is full at that time. When this happens, we assume that the blocked job is held at the server of the queue where it just completed service, blocking that server until the destination can accommodate it. This is called transfer blocking or blocking after service. We also assume that an external arrival that finds a full queue is lost. We consider an open queueing network with inter-arrival times of external arrivals and service times at each queue having a generalized exponential (GE) distribution. Queues can have finite buffers. To solve this system we augment the network by adding a "holding node" for every stream that can be blocked to hold the blocked jobs during the period corresponding to them blocking the server. The mean time spent in the holding node will be equal to that spent while being blocked. Also, to account for the increased service time of a blocked job as seen by customers behind it in the queue, the service times of these customers need to be increased. We thus use an iterative procedure to converge on to the parameters of the GE distributions of the inter-arrival and service time distributions. Results from our analysis are compared against simulations and they compare very well.