Multiple Vacation Policy Research Articles

Algorithmic modelling of a complex redundant multi-state system subject to multiple events, preventive maintenance, loss of units and a multiple vacation policy through a MMAP

Algorithmic modelling of a complex redundant multi-state system subject to multiple events, preventive maintenance, loss of units and a multiple vacation policy through a MMAP

Performance analysis of a versatile bulk-service queue with group-arrival, batch-size-dependent service time and queue-length-dependent vacation

ABSTRACT Queueing systems with bulk-service and vacation policy have become one of the pivotal interest for the researchers due to their widespread application in food processing technology, manufacturing systems, power consumption in small cell base stations etc. This article analyzes a single server versatile bulk-service queueing system wherein the customers arrive according to a compound Poisson process and the service time is dependent on the batch size of undergoing service. Moreover, single and multiple vacation policies have been incorporated along with queue-length-dependent vacation. After providing the steady-state system equations, the bivariate probability generating function of queue and server content distribution together has been derived at departure epoch. After the evaluation of the unknown probabilities, complete joint distributions have been extracted in terms of roots of the denominator of the bivariate probability generating function. The discussed procedure and the reported results have been depicted through some numerical examples for different service and vacation time distributions. Some significant observation about the model has been sketched graphically.

A single server finite buffer Geom/G/1/K queue with L limited service and multiple vacation policy

A single server finite buffer Geom/G/1/K queue with L limited service and multiple vacation policy

Modeling and analysis for a repairable system with multi-state components under K-mixed redundancy strategy

In this paper, a three components repairable system with K-mixed redundancy strategy is proposed, in which the lifetimes of components, the repair time of failure components and the vacation time are distributed with different phase-type (PH) distributions. The different phases can represent different operational levels, repair levels and vacation levels. The multiple vacation policy is also adopted so that the human resources can be fully utilized. The repairable system is studied in both transient and stationary regimes with the matrix-analytic method, and not only some traditional reliability indexes are obtained, but also several new reliability indexes are obtained by employing Kronecker operator theory and aggregated stochastic theory. Finally, a numerical example is implemented to illustrate the results obtained in the paper.

Reliability analysis for multi-state systems under K-mixed redundancy strategy considering switching failure

In this paper, a three components repairable system under K-mixed redundancy strategy with unreliable switching failure is proposed, in which the lifetimes of components, the repair time of failure components and the vacation time are distributed with different phase-type (PH) distributions. The multiple vacation policy of the repairman is adopted so that the human resources can be fully utilized. The proposed repairable system model is studied in both transient and stationary regimes with matrix-analytic method. Some reliability indexes are obtained by employing Kronecker operator theory and aggregated stochastic theory. Finally, a numerical example and a comparison analysis between K-mixed redundancy strategy model and mixed redundancy strategy model are implemented to illustrate the results obtained in the paper.

MMAPs to Model Complex Multi-State Systems with Vacation Policies in the Repair Facility

Two complex multi-state systems subject to multiple events are built in an algorithmic and computational way by considering phase-type distributions and Markovian arrival processes with marked arrivals. The internal performance of the system is composed of different degradation levels and internal repairable and non-repairable failures can occur. Also, the system is subject to external shocks that may provoke repairable or non-repairable failure. A multiple vacation policy is introduced in the system for the repairperson. Preventive maintenance is included in the system to improve the behaviour. Two types of task may be performed by the repairperson; corrective repair and preventive maintenance. The systems are modelled, the transient and stationary distributions are built and different performance measures are calculated in a matrix-algorithmic form. Cost and rewards are included in the model in a vector matrix way. Several economic measures are worked out and the net reward per unit of time is used to optimize the system. A numerical example shows that the system can be optimized according to the existence of preventive maintenance and the distribution of vacation time. The results have been implemented computationally with Matlab and R (packages: expm, optim).

Performance analysis for Bernoulli feedback queues subject to disasters: a system with batch Poisson arrivals under a multiple vacation policy

ABSTRACT We analyze an M/G/1 system with batch Poisson arrivals and instantaneous Bernoulli feedback, operating under a Multiple Vacation Policy. The system is subject to disasters that occur according to an independent Poisson process and are followed by (random) repair periods with general distribution. The analysis is carried out using the supplementary variable method. The Laplace transform of the time between two consecutive disasters is obtained and the existence of the stationary regime for the system is shown. Besides obtaining the stationary distribution for the number of customers in the system, we use the information regarding the rates of occurrence of various events provided by the supplementary variable solution to obtain a great variety of additional results. These include the Laplace transform of the busy period distribution and the probability that a customer completes service. We indicate areas of application of our model to real-life systems, in particular in Vehicle ad hoc Networks (VANETs), and we use the analytic results obtained to optimize such a system under a Quality of Service constraint. Finally, we analyze a variant of the system subject to disasters even when the server is not busy.

Age of Information in Energy Harvesting Aided Massive Multiple Access Networks

Given the proliferation of the massive machine type communication devices (MTCDs) in beyond 5G (B5G) wireless networks, energy harvesting (EH) aided next generation multiple access (NGMA) systems have drawn substantial attention in the context of energy-efficient data sensing and transmission. However, without adaptive time slot (TS) and power allocation schemes, NGMA systems relying on stochastic sampling instants might lead to tardy actions associated both with high age of information (AoI) as well as high power consumption. For mitigating the energy consumption, we exploit a pair of sleep-scheduling policies, namely the multiple vacation (MV) policy and start-up threshold (ST) policy, which are characterized in the context of three typical multiple access protocols, including time-division multiple access (TDMA), frequency-division multiple access (FDMA) and non-orthogonal multiple access (NOMA). Furthermore, we derive closed-form expressions for the MTCD system’s peak AoI, which are formulated as the optimization objective under the constraints of EH power, status update rate and stability conditions. An exact linear search based algorithm is proposed for finding the optimal solution by fixing the status update rate. As a design alternative, a low complexity concave-convex procedure (CCP) is also formulated for finding a near-optimal solution relying on the original problem’s transformation into a form represented by the difference of two convex problems. Our simulation results show that the proposed algorithms are beneficial in terms of yielding a lower peak AoI at a low power consumption in the context of the multiple access protocols considered.

Study on Transient Queue-Size Distribution in the Finite-Buffer Model with Batch Arrivals and Multiple Vacation Policy.

The transient behavior of the finite-buffer queueing model with batch arrivals and generally distributed repeated vacations is analyzed. Such a system has potential applications in modeling the functioning of production systems, computer and telecommunication networks with energy saving mechanism based on cyclic monitoring the queue state (Internet of Things, wireless sensors networks, etc.). Identifying renewal moments in the evolution of the system and applying continuous total probability law, a system of Volterra-type integral equations for the time-dependent queue-size distribution, conditioned by the initial buffer state, is derived. A compact-form solution for the corresponding system written for Laplace transforms is obtained using an algebraic approach based on Korolyuk’s potential method. An illustrative numerical example presenting the impact of the service rate, arrival rate, initial buffer state and single vacation duration on the queue-size distribution is attached as well.

Stationary joint distribution of a discrete-time group-arrival and batch-size-dependent service queue with single and multiple vacation

Discrete-time queueing systems have widespread applications in packet switching networks, internet protocol, Broadband Integrated Services Digital Network (B-ISDN), circuit switched time-division multiple access etc. In this paper, we analyze an infinite-buffer discrete-time group-arrival queue with single and multiple vacation policy where processing/transmission/service times dynamically vary with batch-size under service. The bivariate probability generating function of queue length and server content distribution has been derived first, and from that we extract the joint probabilities in terms of roots of the characteristic equation. We also find the joint distribution at arbitrary and pre-arrival slot. Discrete phase type distribution plays a noteworthy role in order to regulate the high transmission error through a particular channel. In view of this, numerical illustrations include the service time distribution to follow the discrete phase type distribution.

Optimizing a Multi-State Cold-Standby System with Multiple Vacations in the Repair and Loss of Units

A complex multi-state redundant system with preventive maintenance subject to multiple events is considered. The online unit can undergo several types of failure: both internal and those provoked by external shocks. Multiple degradation levels are assumed as both internal and external. Degradation levels are observed by random inspections and, if they are major, the unit goes to a repair facility where preventive maintenance is carried out. This repair facility is composed of a single repairperson governed by a multiple vacation policy. This policy is set up according to the operational number of units. Two types of task can be performed by the repairperson, corrective repair and preventive maintenance. The times embedded in the system are phase type distributed and the model is built by using Markovian Arrival Processes with marked arrivals. Multiple performance measures besides the transient and stationary distribution are worked out through matrix-analytic methods. This methodology enables us to express the main results and the global development in a matrix-algorithmic form. To optimize the model, costs and rewards are included. A numerical example shows the versatility of the model.

English

English

Analysis of unreliable bulk queueing system with overloading service, variant arrival rate, closedown under multiple vacation policy

Analysis of unreliable bulk queueing system with overloading service, variant arrival rate, closedown under multiple vacation policy

Analysis of unreliable bulk queueing system with overloading service, variant arrival rate, closedown under multiple vacation policy

Analysis of unreliable bulk queueing system with overloading service, variant arrival rate, closedown under multiple vacation policy

Variant vacation queueing system with Bernoulli feedback, balking and server's states-dependent reneging

We consider a single server Markovian feedback queue with variant of multiple vacation policy, balking, server?s states-dependent reneging, and retention of reneged customers. We obtain the steady-state solution of the considered queue based on the use of probability generating functions. Then, the closed-form expressions of different system characteristics are derived. Finally, we present some numerical results in order to show the impact of the parameters of impatience timers on the performance measures of the system.

Analysis and Performance Evaluation of Markovian Feedback Multi-Server Queueing Model with Vacation and Impatience

This paper deals with a finite capacity multi-server Markovian queueing model with Bernoulli feedback, synchronous multiple vacation policy and customers’ impatience (balking and reneging). By employing certain customer retention mechanism, impatient customers can be retained in the system. Applications of the suggested queueing model can be found in a wide variety of practical systems including modern information and communication technology (ICT) networks, call centers, and manufacturing systems. Using the recursive method, the steady state probabilities of the model are obtained. Various performance measures are derived. Then, some important particular cases are provided. Finally, different numerical examples are presented to demonstrate how the different parameters of the model influence the behavior of the stationary characteristics of the system.

Queuing Analysis on Multiple Vacation Policies and Reneging

We study a non markovian queue which renders service to the customers. After the completion of service the server ought to go for the compulsory vacation stage by stage in succession. We consider one of the customer’s behaviors reneging to occur when the server’s vacation is extended. Using Supplementary variable technique the system performance measures is derived.

Effects of Catastrophe on a Queueing System with Voice over Internet Protocol

Consider a retrial queue with VoIP calls and two kinds of heterogeneous services such as essential and optional services. The multiple vacation policy, retrial policy, customer’s impatience and the concept of catastrophe are adopted to derive the required solutions. The steady state system size distribution and probability generating function under different level have been obtained. Based on some assumptions, special and particular cases are discussed.

Analytical Model of a Wireless Sensor Network (WSN) Node Operation with a Modified Threshold-Type Energy Saving Mechanism.

In this article, a model of the operation of a wireless sensor network (WSN) node with an energy saving mechanism based on a threshold-controlled multiple vacation policy is considered. When the queue of packets directed to the node becomes empty, a multiple vacation period is started during which the receiving/transmitting of packets is blocked. In such a period, successive vacations of a fixed constant duration are taken until a predetermined number of N packets accumulated in the queue is detected. Then, at the completion epoch of this vacation, the processing restarts normally. The analytic approach is based on the conception of an embedded Markov chain; integral equations and renewal theory are applied to study the queue-size transient behaviour. The representations for the Laplace transforms of the queue-size distribution at an arbitrary fixed time t and on the idle and processing periods are obtained. The compact-form formulae for the distributions of the idle and processing period duration are derived. Numerical examples are attached as well.

Distribution of the time to buffer overflow in the M/G/1/N-type queueing model with batch arrivals and multiple vacation policy

A single-channel FIFO queueing model with finite buffer capacity and the multiple vacation policy is investigated, in which jobs arrive according to a compound Poisson process and are being processed individually with a general-type distribution function of the service time. A multiple vacation period, consisting of a number of independent generally-distributed server vacations, is being started each time when the system becomes empty. During this period, the processing of jobs is suspended. Successive server vacations are being initialised until at least one job is present in the buffer at the completion epoch of one of them. A compact formula for the Laplace transform of the distribution of the time to the first buffer overflow, conditioned by initial number of packets present in the buffer, is found. The analytical approach is based on the paradigm of embedded Markov chain, integral equations and Korolyuk’s potential idea. Numerical illustrating examples are attached as well.