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.

Optimization Strategies for Dockless Bike Sharing Systems via two Algorithms of Closed Queuing Networks

The dockless bike sharing system (DBSS) has been globally adopted as a sustainable transportation system. Due to the robustness and tractability of the closed queuing network (CQN), it is a well-behaved method to model DBSSs. In this paper, we view DBSSs as CQNs and use the mean value analysis (MVA) algorithm to calculate a small size DBSS and the flow equivalent server (FES) algorithm to calculate the larger size DBSS. This is the first time that the FES algorithm is used to study the DBSS, by which the CQN can be divided into different subnetworks. A parking region and its downlink roads are viewed as a subnetwork, so the computation of CQN is reduced greatly. Based on the computation results of the two algorithms, we propose two optimization functions for determining the optimal fleet size and repositioning flow, respectively. At last, we provide numerical experiments to verify the two algorithms and illustrate the optimal fleet size and repositioning flow. This computation framework can also be used to analyze other on-demand transportation networks.

Performance Analysis and Improvement of the Bike Sharing System Using Closed Queuing Networks with Blocking Mechanism

The Bike Sharing System is a sustainable urban transport solution that consists of a fleet of bikes placed in various stations. Users will be satisfied if they find available bikes at their departure station and free docks at the destination. Despite the regulation operations of the system provider (i.e., redistribution of bikes by truck) deeper modifications (bike fleet size or station capacity) are often necessary to ensure a satisfactory service rate. In this paper, we model a sub-graph of a Bike Sharing System using the closed queuing network with a Repetitive-Service-Random-Destination blocking mechanism. This model is solved using the Maximum Entropy Method. This model faithfully reproduces the system dynamics considering the limited capacity of stations. We analyze the performance, particularly, via an overall performance indicator of the system. The various control and monitoring decisions (fleet-size, capacity of stations, incoming and outgoing flow of bikes) are applied to find out the best performance levels. The results demonstrate that the overall performance is robust enough regarding the fleet size changes but it degrades with the increase of the stations’ capacity. Finally, the arrival and departure flows control is an efficient and powerful operational leverage.