Optimal Choice of Server’s Number and the Various Control Rules for Systems with Moving Servers

Abstract

AbstractIn the paper the new mathematical models, describing a wide class of the systems with moving servers are constructed. The prototypes of such systems are communication and network systems, lifts’ systems, data processing systems, traffic and others. In the capacity of the examples of the systems with moving servers’ the lifts’ systems are considered. As the efficiency indices a customer average waiting (CWT) and service times (CST) are taken. For some cases, using the methods of stochastic processes and queuing theory, the analytical result for finding an optimal number of servers, minimizing CWT has been derived. These results allow to make useful recommendations for planning systems with moving servers. The various control rules by these systems are introduced and investigated. Using Wolfram Mathematica, there were created the new programs for simulation of complicated systems with moving servers. The graphs, demonstrating operating of these systems are shown. Investigation the various control rules showed an advantage some of them. Numerical results, allowing to compare the various control rules and depending the lift roominess on intensity of input flow are given.KeywordsSystem with moving serversOptimal number of serversLifts’ systemsControl by lifts’ systemsLoading and unloading regimesA customer average waiting and service times