Arrival Queue Research Articles

M^x/G/1FEEDBACK QUEUE WITH THREE STAGE HETEROGENEOUS SERVICE, MULTIPLE ADAPTIVE VACATION AND CLOSED DOWN TIMES

We consider a batch arrival queueing system with three stage heterogeneous service provided by a single server with different (arbitrary) service time distributions. Each customer undergoes three stages of heterogeneous service. As soon as the completion of third stage of service, if the customer is dissatisfied with his service, he can immediately join the tail of the original queue. The vacation period has two heterogeneous phases. After service completion of a customer the server may take a phase one Bernoulli vacation. Further, after completion of phase one Bernoulli vacation the server may take phase two optional vacation. The vacation times are assumed to be general. In addition we assume restricted admissibility of arriving batches in which not all batches are allowed to join the system at all times. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been obtained explicitly. Also the mean number of customers in the queue and the system are also derived. Some particular cases and numerical results are discussed.

DISCRETE-TIME GIX/GEO/1/N QUEUE WITH WORKING VACATIONS AND VACATION INTERRUPTION

In this paper, we study a discrete-time finite buffer batch arrival queue with multiple geometric working vacations and vacation interruption: the server serves the customers at the lower rate rather than completely stopping during the vacation period and can come back to the normal working level once there are customers after a service completion during the vacation period, i.e., a vacation interruption happens. The service times during a service period, service times during a vacation period and vacation times are geometrically distributed. The queue is analyzed using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at pre-arrival, arbitrary and outside observer's observation epochs. We also present probability generation function (p.g.f.) of actual waiting-time distribution in the system and some performance measures.

Performance analysis of a batch arrival retrial queue with Bernoulli feedback

This paper facilitates the performance prediction of an M X /G/1 retrial queue wherein the single server follows a modified vacation policy . We assume that the job who finds the server busy joins the retrial group (orbit) to get its service in random order and only the job at the head of the queue is allowed to receive service from the server first. As soon as the system becomes empty, the server leaves for at most J vacations of random length V each. When the server returns from the vacation and finds at least one job in the orbit, it renders service to these jobs otherwise it goes for next vacation. We assume that the service time, retrial time and vacation times are general distributed. The balking behaviour of the jobs is also taken into consideration. By using supplementary variable technique, we derive the formulas for system size distribution and mean system size at departure points and other performance measures. Numerical illustrations have been provided to validate the analytical results. In addition, by setting appropriate parameters, some special cases are deduced which tally with existing results. Tables and figures have been facilitated to examine the system behaviour with regard to different parameters.

Non-Markovian bulk queueing system with state dependent arrivals and multiple vacations - a simulation approach

We considered a non-Markovian bulk arrival general bulk service queueing system with state dependent arrivals and multiple vacations in this paper. The arrivals occur in bulk with a rateλ, when the server is busy and with a rateλ0, when the server is on vacation. Using a supplementary variable technique and difference differential equations method we derive the queue size distribution, expected length of idle and busy periods and expected queue size of a Mx/G(a, b)/1 queueing system with state dependent arrivals and multiple vacations. We study the same through simulation using ARENA, a powerful manufacturing system simulation software and obtained some performance measures, which are mandatory for the study and analysis of the said queueing model. The simulated results for a few cases are presented.

An M/G/1 two phase multi-optional retrial queue with Bernoulli feedback, non-persistent customers and breakdown and repair

This paper has been motivated by the interactive voice response system (IVRS). This system has now become a common phenomenon in our everyday life. In this paper, we consider a Poisson arrival queueing system with a single server and two essential phases of heterogeneous service. The customer who completes the first phase has a choice of k-options to choose for the second phase of service. The customer, who finds the server busy upon arrival, can either join the orbit or he/she can leave the system. After completion of both phases, the customer can decide to try again for service by joining the orbit or he/she can leave the system. The server is subject to sudden breakdowns and repairs. We assume that the breakdowns of the system can occur even when the system is idle. By using the supplementary variables technique, we have obtained the steady state probability generating functions of the orbit size and the system size. We obtain a stochastic decomposition law for the system. We present numerical results ...

A Non-Markovian Multistage Batch Arrival Queue with Breakdown and Reneging

The present investigation deals with analysis of non-Markovian queueing model with multistage of services. When the server is unavailable during the system breakdown (or) vacation periods, we consider reneging to prevail. Supplementary variable techniques have been adopted to obtain steady state system length distributions. The numerical illustrations are provided to validate the tractability of performance measures as far as computational aspect is concerned. Numerical results in the form of graphical representation are also presented. Practical large scale industry applications are described to justify our model.

Queueing model with non-homogeneous bulk arrivals having state-dependent service rates

This paper considers a single-server queueing model with non-homogeneous bulk arrivals and state-dependent service rates. The bulk arrival queueing model is important in developing optimal operating policies for queueing in transportation systems and communication systems. Arrivals are assumed to be characterised by a non-homogeneous compound Poisson process, and the service rate depends on the content of the buffer connecting to the service station. Using difference-differential equations and a probability generating function, the system’s behaviour is analysed. Explicit expressions are derived for performance measures including average number of customers in the queue and probability of queue emptiness, etc. Sensitivity analysis of the model revealed that assuming non-homogeneous arrival significantly influences the system performance measures. The state-dependent service rate strategy can control queue congestion and mean delay in transmission. This model is effective in evaluating the performance of time-dependent communication systems.

Batch arrival queueing system with two stages of service

This Paper studies batch arrival queue with two stages of service. Random breakdowns and Bernoulli schedule server vacations have been considered here .After a service completion, the server has the option to leave the system or to continue serving customers by staying in the system. It is assumed that customers arrive to the system in batches of variable size, but served one by one. After completion of first stage of service, the server must provide the second stage of service to the customers. Vacation time follows general distribution, while we consider exponential distribution for repair time.We obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, average number of customers ,and the average waiting time in the queue.

A Batch Arrival Single Server Queue with Server Providing General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns

We study the behavior of a batch arrival queuing system equipped with a single server providing general arbitrary service to customers with different service rates in two fluctuating modes of service. In addition, the server is subject to random breakdown. As soon as the server faces breakdown, the customer whose service is interrupted comes back to the head of the queue. As soon as repair process of the server is complete, the server immediately starts providing service in mode 1. Also customers waiting for service may renege (leave the queue) when there is breakdown or when server takes vacation. The system provides service with complete or reduced efficiency due to the fluctuating rates of service. We derive the steady state queue size distribution. Some special cases are discussed and numerical illustration is provided to see the effect and validity of the results.

On The Renewal Input Batch-arrival Queue Under Single And Multiple Working Vacation Policy With Application To EPON

This paper analyzes renewal input batch arrival queues with multiple and single working vacation policy. We obtain the steady state system-length distributions at pre-arrival and arbitrary epochs. The Laplace-Stieltjes transforms (LST) of the sojourn time distribution for the first customer and an arbitrary customer in an accepted batch have been derived. Also the probability density function of sojourn time distribution for the first customer in an accepted batch has been obtained. The proposed analysis is based on the roots of the characteristics equations formed using the probability generating functions (p.g.f.) of embedded pre-arrival epoch probabilities. Several performance measures such as the mean system-length and mean sojourn times of first and an arbitrary customer in an accepted batch are presented. The suggested queues have potential application in ethernet passive optical network (EPON).

예약도착 대기행렬을 활용한 함정정비 최적 예약시간 산정에 관한 연구

Queueing system with scheduled arrivals is useful in many fields where both customers' waiting time and servers' operation time (utilization) are important, and arrival time of customers is possible to be controlled. In this paper, we analyzed the operation of ship maintenance with the queueing system with scheduled arrival. Based on the model presented by Pegden and Rosenshine [8], who dealt with exponential service time, we extended the service time distributions to phase-type distribution which is able to include a wide range of real stochastic phenomena. Since most activities in the military are carried out under tight control and schedule, scheduled arrival queue has quite good applicability in this area. In this context, we applied queue with scheduled arrival to the optimal booking time decision for the ship maintenance in the navy.

Note on a Binomial Schedule for an MX/G/1 Queueing System with an Unreliable Server

We consider in this paper a batch arrival queueing system with an unreliable server. If the queue is empty at a service completion, then the server becomes inactive and begins an idle period. However, if the queue is not empty, then the server will take at most vacation before serving the next customer. A linear cost structure is developed for the system and the optimal value of is obtained.

A simple policy for multiple queues with size-independent service times

We consider a service system with two Poisson arrival queues. A server chooses which queue to serve at each moment. Once a queue is served, all the customers will be served within a fixed amount of time. This model is useful in studying airport shuttling or certain online computing systems. We propose a simple yet optimal state-independent policy for this problem which is not only easy to implement, but also performs very well.

Congestion Prediction and Adaptive Rate Adjustment Technique for Wireless Sensor Networks

In general, nodes in Wireless Sensor Networks (WSNs) are equipped with limited battery and computation capabilities but the occurrence of congestion consumes more energy and computation power by retransmitting the data packets. Thus, congestion should be regulated to improve network performance. In this paper, we propose a congestion prediction and adaptive rate adjustment technique for Wireless Sensor Networks. This technique predicts congestion level using fuzzy logic system. Node degree, data arrival rate and queue length are taken as inputs to the fuzzy system and congestion level is obtained as an outcome. When the congestion level is amidst moderate and maximum ranges, adaptive rate adjustment technique is triggered. Our technique prevents congestion by controlling data sending rate and also avoids unsolicited packet losses. By simulation, we prove the proficiency our technique. It increases system throughput and network performance significantly..

A soft computing-based approach to optimise queuing-inventory control problem

In this paper, a multi-product continuous review inventory control problem within batch arrival queuing approach (MQr/M/1) is developed to find the optimal quantities of maximum inventory. The objective function is to minimise summation of ordering, holding and shortage costs under warehouse space, service level and expected lost-sales shortage cost constraints from retailer and warehouse viewpoints. Since the proposed model is Non-deterministic Polynomial-time hard, an efficient imperialist competitive algorithm (ICA) is proposed to solve the model. To justify proposed ICA, both ganetic algorithm and simulated annealing algorithm are utilised. In order to determine the best value of algorithm parameters that result in a better solution, a fine-tuning procedure is executed. Finally, the performance of the proposed ICA is analysed using some numerical illustrations.

Transient Solution of an Batch arrival Queue with Two Types of Service, Multiple Vacation, Random breakdown and Restricted Admissibility

In this paper we analyse a batch arrival queue with two types of service subject to random breakdowns having multiple server vacation. We assume that the server provides two types of service, type 1 with probability and type 2 with probability with the service times following general distribution and each arriving customer may choose either type of service. The server takes vacation each time the system becomes empty and the vacation period is assumed to be general. On returning from vacation if the server finds no customer waiting in the system, then the server again goes for vacation until he finds at least one customer in the system. The system may breakdown at random and repair time follows exponential distribution. In addition we assume restricted admissibility of arriving batches in which not all batches are allowed to join the system at all times. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been obtained explicitly. Average queue lenth and average system size are also computed.

An MX/G/1 queue with randomized working vacations and at most J vacations

This paper treats a bulk arrival queue with randomized working vacation policy. Whenever the system becomes empty, the server takes a vacation. During the vacation period, customers are to be served at a lower rate. Once the vacation ends, the server will return to the normal working state and begin to serve the customers in the system if any. Otherwise, the server either remains idle with probability p or leaves for another vacation with probability 1−p. This pattern continues until the number of vacations taken reaches J. If the system is empty at the end of the Jth vacation, the server will wait idly for a new arrival. By using supplementary variable technique, we derive the system size distribution at arbitrary epoch, at departure epoch and at busy period initial epoch, as well as some important system characteristics. Numerical examples are provided to illustrate the influence of system parameters on several performance measures.

Sample-path analysis of general arrival queueing systems with constant amount of work for all customers

We consider a discrete-time queueing system where the arrival process is general and each arriving customer brings in a constant amount of work which is processed at a deterministic rate. We carry out a sample-path analysis to derive an exact relation between the set of system size values and the set of waiting time values over a busy period of a given sample path. This sample-path relation is then applied to a discrete-time $$G/D/c$$ queue with constant service times of one slot, yielding a sample-path version of the steady-state distributional relation between system size and waiting time as derived earlier in the literature. The sample-path analysis of the discrete-time system is further extended to the continuous-time counterpart, resulting in a similar sample-path relation in continuous time.

Analysis of M X / G /1 feedback queuewith two-phase service, compulsory server vacation and random breakdowns

This paper investigates a batch arrival queueing system with two-phase heterogeneous service under compulsory vacation schedule. Upon arrival any batch that finds the server busy, on vacation or under repair joins the queue. Otherwise one customer from the arriving batch enters the server for service immediately while the rest join the queue. After completion of the second phase of service for each customer, the server goes for a vacation. Busy servers are interrupted by breakdowns and repair has to be done to resume service. If a customer is unsatisfied with his service he is allowed to join the tail of the queue as a feedback customer. We construct the mathematical model and derive the probability generating functions of transient state probabilities in terms of their Laplace transforms. The steady state distributions of the server state are deduced and the average number of customers in the system, the mean waiting time of a customer are obtained. Particular cases of interest of the model are discussed in order to verify the results. Numerical computations are provided to visualize the effect of parameters on system performance measures and also to validate our analytical results.

On parallel and series non homogeneous bulk arrival queueing model

Queueing models create lot of importance due to their ready applicability. Much work has reported in literature regarding queueing models with homogeneous Poisson arrivals. But in many practical situations arising at places like transportation, communication networks, production processes, etc., the arrivals are non homogeneous and time dependent. Hence, in this paper we develop and analyze a queueing model with non homogeneous (time dependent) bulk arrivals under parallel and series configuration. Using the difference differential equations the joint probability density function of the number of customers in each queue is obtained. The performance of the model is evaluated by deriving the explicit expressions of the system characteristics like the probability of the system emptiness, average number of customers in each queue, the mean waiting time of the customer, the throughput of the nodes, etc. The sensitivity analysis of the model revealed that the bulk size distribution parameters and non homogeneous arrivals have significant influence on the system performance measures. The utility of the model in congestion control is demonstrated through a numerical illustration.