Closed Queuing Network Model Research Articles

Approximate analysis of general open queuing networks with restricted capacity

We consider an open queuing network having general service time distributions. The total number of customers simultaneously present in the network connot exceed a given value, called the capacity of the network. Customers arriving while the network is full are forced to wait in an external queue. We present an approximate analysis of such queuing networks. We first derive an equivalent closed queuing network model. This closed model is analyzed using an approximate product-form solution technique. The performance parameters of the original open model are then easily derived. We compare this method with the classical aggregation technique.

The optimality of balancing workloads in certain types of flexible manufacturing systems

Symmetric mathematical programming is used to analyze the optimality of balancing workloads to maximize the expected production in a single-server closed queuing network model of a flexible manufacturing system (FMS). In particular, using generalized concavity we prove that, even though the production function is not concave, balancing workloads maximizes the expected production in certain types of m-machine FMS's with n parts in the system. Our results are compared and contrasted with previous models of production systems.

Maximum-Entropy Principle in Flexible Manufacturing Systems

It is shown that the entropy of the joint probability distribution of the queue lengths of the M machine-groups in a closed queuing network model of a flexible manufacturing system is maximum when the loads on the different machine-groups are equal for both single-machine machine-groups and for those multiple-machine machine-groups of which group sizes are equal. It is also shown that for unequal machine-group-sizes, the entropy is not maximum when the workload is balanced. The simultaneous variations of the entropy function of the load distribution, the entropy function of joint probability distribution lengths of queues and the expected production function are studied in order to investigate the relationship between the information content and productive capacity of manufacturing systems. Four measures of load balance in a flexible manufacturing system are given.

Approximating Pre-emptive Priority Dispatching in a Multiprogramming Model

The formulation of the closed queuing network model of a multiprogramming computer system is generalized to allow each task to have its own set of facility service rates and I/O device selection probability distribution. In the model, processor sharing is assumed for different types of customers. It is shown through a series of investigations that the model reasonably approximates preemptive priority dispatching.