On the Application of Mean Value Analysis Without the Normalization Constant in the Closed Queuing Networks

An example of closed queue network could be view when patients arrive at a doctor’s office to update their medical records, then it’s off to the nurse’s station for various measurements like weight, blood pressure, and so on. The next stop is generally to queue (i.e., wait patiently) for one of the doctors to arrive and begin the consultation and examination. Perhaps it may be necessary to have some X-rays taken, an ultrasound may be called for, and so on. After these procedures have been completed, it may be necessary to talk with the doctor once again. The final center through which the patient must pass is always the billing office. In this work, multiple-node” system in which a customer requires service at more than one node, which may be viewed as a network of nodes, and each node is a service center having storage room for queues to form and perhaps with multiple servers to handle customer requests is investigated in order to provide some insight into the performance measure analysis. Our quest is to exempt the normalization constant in the computation of performance measure in the closed queueing network. The arrival properties and Little’s law are use with the help of some existing equations and formulas in queueing network. Performance measures, such as Mean number of customers, response time, throughput, and marginal probability distribution are obtained for central server and load dependent server closed queuing networks for nodes 4 and 5, and also for k = 3 and k = 10.

Modeling of Railway Stations Based on Queuing Networks

Among the micro-logistic transport systems, railway stations should be highlighted, such as one of the most important transport infrastructure elements. The efficiency of the transport industry as a whole depends on the quality of their operation. Such systems have a complex multi-level structure, and the incoming traffic flow often has a stochastic character. It is known that the most effective approach to study the operation of such systems is mathematical modeling. Earlier, we proposed an approach to transport hub modeling using multiphase queuing systems with a batch Markovian arrival process (BMAP) as an incoming flow. In this paper, we develop the method by applying more complex models based on queuing networks that allow us to describe in detail the route of requests within an object with a non-linear hierarchical structure. This allows us to increase the adequacy of modeling and explore a new class of objects—freight railway stations and marshalling yards. Here we present mathematical models of two railway stations, one of which is a freight railway station located in Russia, and the other is a marshalling yard in the USA. The models have the form of queuing networks with BMAP flow. They are implemented as simulation software, and a numerical experiment is carried out. Based on the numerical results, some “bottlenecks” in the structure of the studied stations are determined. Moreover, the risk of switching to an irregular mode of operation is assessed. The proposed method is suitable for describing a wide range of cargo and passenger transport systems, including river ports, seaports, airports, and multimodal transport hubs. It allows a primary analysis of the hub operation and does not need large statistical information for parametric identification.

Long-Term Behavior of Dynamic Equilibria in Fluid Queuing Networks

Steady State in Equilibrium for Flows over Time