Compare Inverse Matrix Between Sequential and Parallel for Multithreading with Queueing Network

This work deals with minimizing the computing time for matrix inversions used in the queueing system models or otherwise. The time is reduced considerably and is proportional to the number of the used threads in parallel

The establishment of the time interval between inspections for a cold standby system with component repair

Abstract The time interval between inspections of cold standby systems is a crucial decision to ensure the appropriated system reliability and the lowest costs possible. This paper presents a model developed to establish the optimal time interval between inspections for a two-unit cold standby system with component repair and subject to periodic inspection, considering reliability and costs. A Markov chain is used to define possible states, their transition probabilities and the mean time to system failure, as a function of the time interval between inspections. Given the mean time to system failure, the steady state availability is determined. Finally, the costs related to the system maintenance are established and a cost function is developed and optimized for the time interval between inspections. Numerical examples are presented and results for different system parameters are compared. Besides optimizing the time interval between inspections, the analyses also reveal the effect of repair time on system availability and mean time to system failure

Analysis of a Priority Controllable Queue MX1,MX2/G1(a,b),G2(a,b)/1 With Multiple Vacations, Setup Times and Closedown Times

In this paper a priority queuing system MX1,MX2/G1(a,b),G2(a,b)/1 with multiple vacations, setup times with N-policy and closedown times has been deduced. Two types of customers, priority and nonpriority, are arrived and are served in this queuing situation. In priority schemes, customers with priority are selected for service ahead of those with nonpriority, independent of their time of arrival into a system, but with no preemption. On completion of service, if each of the number of priority customers ξ1 and the number of nonpriority customers ξ2 in the queue is less than ”a” the server performs closedown work. Following closedown, the server leaves for multiple vacations of random length. When the server returns from a vacation and finds the number of customers of either type in the queue is less than ”N”, he leaves for another vacation and so on, until he finds at least ”N” (N b) customers of either type in the queue waiting for service. Then, he requires a setup time ”R” to start service. After the setup he starts the service with a batch of ”b” from the ”N” priority customers, where b ≥ a. After service, if the number of waiting priority customers ξ1 ≥ a, then the server serves a batch of min (ξ1,b) customers of that type and so on until ξ1 \u3c a, then the server serves non-priority customers in the same way. The probability generating function of the queue size distribution at an arbitrary epoch and various characteristics of the queuing model are derived