Particle Swarm Optimization and Maximum Entropy Results for MX/G/1 Retrial G-Queue with Delayed Repair

Abstract

This paper examines an MX/G/1 retrial model with negative customers including the concepts of working vacation, Bernoulli feedback, delayed repair, state-dependent and multi-optional services. Such a queue is quite relevant in real world, for instance in computer systems, manufacturing organisations, packet-switching networks, telecommunication systems, etc. The arrival pattern of customers is according to Poisson distribution. The service is such that first essential service (FES) is provided to every customer and second optional service (SOS) is provided in k phases to those who wants to opt for the same. The negative customers may arrive during the time when the server is busy in serving a positive customer. This leads to breakdown of the server and thus the server has to be restored (repair) by the repair man. Some moments may be taken by the repair man to initiate the repair process, leading to delay in repair. In our work, firstly we have calculated performance measures like long run probabilities and orbit size along with some reliability indices. Then a relative study between the exact expected waiting time and approximate expected waiting time of the system is presented via maximum entropy approach. Also we perform cost optimization using particle swarm optimization (PSO method). Few numerical results are also provided.

Kullback-Leibler Divergence(KLD) Formalism of The Stable Queue with KLD Applications to Biometrics

“…which is the obtained Shannonian formalism in [20]. This shows the strength of the newly devised KLD formalism.…”

“…It is observed that as 𝑞(0) → 1 , τ → τ , which reduces to the Shannonian limiting case obtained (c,f., [20]). Corollary 1.…”

“…According to [18][19][20], the maximum entropy state probability of the generalized geometric solution of a stable M/G/1 queue, subject to normalization, mean queue length (MQL), L and server utilization, 𝜌(<1) is given by: where 𝑔 = ( )( ) , 𝑥 = and 𝐿 = 1 + (MQL for the underlying queue), 𝜌 (= 1 -𝑝(0)) and 𝐶 is the squared coefficient of variations). Obviously, 𝑝(𝑛) (c.f., (3)) reads:…”

Trajectory Tracking of Soccer Motion Based on Multiobject Detection Algorithm

“…When there were obstacles on the optimal path, they sought a new path through a turning point setting to reduce the system resources consumed by the algorithm. As the demand for robot intelligence increases, the environment it faces becomes more and more complex, and the focus of path planning research gradually turns to application research in the complex dynamic environment [11].…”

Intelligent Electrical Engineering Automation on Account of Particle Swarm Optimization (PSO) Algorithm

“…The optimization design of electrical products is a skill with great theoretical and technical difficulties. The design of electrical products requires a full combination of advanced theoretical knowledge in the field and the expertise of outstanding scholars [12][13]. At the same time, the above work will be completed, excellent electrical products will be designed.…”