Bulk Arrivals Research Articles

Simulation model for extended double-ended queueing

The purpose of this paper is to extend traditional double-ended queuing models using a simulation approach. Traditional double-ended queuing models assume that one supply queue should satisfy one demand queue through instantaneous pairing. Inter-arrival time is assumed to follow an exponential distribution, with arrivals to the system assumed to occur just one at a time. However, this assumption is frequently violated in many real-world situations. The pairing or batch size can either be multiple or a random variable, and the pairing processing time can be greater than 0. Inter-arrival time may follow distributions other than exponential. In some cases bulk arrivals may come at the same time, and pairing is not always guaranteed. Because the analytical approach has enormous difficulties obtaining performance measures under these relaxed situations, a simulation approach for extended double-ended queueing processes is presented. This includes an algorithm to find state probabilities and a newly developed simulation procedure. Using this new procedure, sensitivity analyses of performance measures were performed using various input conditions implemented using ProModel and SimRumnner simulation software. A business case is studied to demonstrate the versatility of the proposed approaches.

Queue-Length Analysis of Continuous-Time Polling System with Vacations Using M-Gated Services

In this paper we consider the polling system with multiple vacations an bulk arrival using M-gated services in continuous time. By the imbedded Markov chain theory, the generating functions of queue length at the station is obtained. Then computational equations are explicitly determined for the mean queue length. Especially we can obtain some corresponding results under some especial cases. The results reveal that our system model can guarantee better QoS and system stability, and it has better efficiency than that of traditional gated service.

A discrete-time queueing network model of a hub-based OBS architecture

We propose and analyze a novel discrete-time queueing network model of a zero loss hub-based Optical Burst Switched (OBS) architecture, consisting of multiple input edge nodes and one destination edge node. The arrival process of bursts is slotted with bulk arrivals as generated by a Time and Burst-Length based burst aggregation algorithm. The queueing network is analyzed by decomposition. We obtain the average end-to-end delay of a burst in the queueing network as well as queueing delays at individual nodes. Our model provides a tight upper bound as shown by comparing the analytical data to simulation results.

A diffusion approximation for batch queues of type [formula omitted

Queues with bulk arrivals and batch service arise in a variety of application areas, in particular in the performance analysis of manufacturing lines, like semiconductor fabrications. In the course of this paper, a diffusion approximation for queueing systems with bulk arrivals and batch service for general and independent interarrival time distributions, as well as general service time distributions, is presented. The approximation uses a modified absorbing barrier and instantaneous return approach. The accuracy of the gained approximation is shown by a subsequent comparison with the corresponding discrete event simulation results.

Performance analysis of non-preemptive GE/G/1 priority queueing of LER system with bulk arrivals

M X / G / 1 non-preemptive priority queue with bulk arrivals has already been analysed in many papers. Two problems are known in this area: first, when the number of priorities is greater than 2, the analysis for priority processes is obviously very difficult to handle. Therefore, the earlier work on the subject was restricted mostly to two priority classes; and second, although analytically explicit results are available, they require sophisticated closed-form expressions of the mean queue length. One particular bulk size distribution – the GE distribution – is motivated by an ME (Maximum Entropy) formulation for the behavior of a G/G/1 queue. The choice of a GE distribution is motivated by the fact that measurements of actual inter-arrival traffic or service times may be generally limited and so only few parameters, such as mean and variance, can be computed reliably. Thus this paper we can obtain very simple and analytic closed-form expression for the mean queue length of a GE/G/1 priority queue and a significant increase in performance evaluation has been achieved. We present the four-class priority queues, performance analysis and simulation of the LER (Label Edge Router) system in the ATM-based MPLS (Multiprotocol Label Switching) network. We wish to obtain the boundary conditions of the mean queue lengths and the mean queueing delays for each priority class, since this metric is one of the most important in performance evaluation parameters for improving QoS and system performance of the LER system in ATM-based MPLS network. A significant numerical example is presented and discussed as well. In order to obtain optimizing the performance analysis for EF flow, AF 1 flow, AF 2 flow and BE flow, the optimum ratios of COV (Coefficient of Variation) can be found via many numerical experiments carried out by the authors for queueing network model with HOL (Head of Line) priority rules. However, the ratios of COV value constraints exist. Furthermore, we find that each service class gradually begins to deteriorate when SQVs (Squared Coefficient of Variations), C ai 2 > 15.524 , C si 2 > 12.96 and traffic intensity is greater than 0.95. We also find the values of maximum allowed burst size for EF flow and AF 1 flow and perform necessary policing actions on EF flow and AF 1 flow at the boundary node of the network. Finally, the four-class GE/G/1 priority queues and performance analysis of the LER system are shown accurate and robust after the comparison between theoretical evaluates and computer simulation results.

A Study of a Merging Section of PRT System with Bulk Arrival and its Control Strategy

This paper deals with a merging section of Personal Rapid Transit system with bulk arrival. Vehicles arrive at a merging section from a main line and a sub line. In most of the previous studies on PRT system, vehicles on the main line have priority. Then, a queue is formed only on the sub line. In this situation, the queuing delay on the sub line may become extremely long. We propose a control strategy whereby vehicles on the main line are not stopped in normal situation; vehicles on the main line are only stopped when the number of waiting vehicles on the sub line exceeds some specific number. This specific number is a sort of threshold. Thus, queues are formed on the main line and the sub line, respectively. Both of the queuing delays are controlled with the threshold. The optimal value of the threshold can be obtained by analyzing the stochastic model. By the optimal value, we can set the rate of queuing delay between the main and sub lines to an arbitrary rate.

Transparent Scheduling of Composite Web Services

Composite Web Services (CWS) aggregate multiple Web Services in one logical unit to accomplish a complex task (e.g. business process). This aggregation is achieved by defining a workflow that orchestrates the underlying Web Services in a manner consistent with the desired functionality. Since CWS can aggregate atomic and other CWS they foster the development of service layers and reuse of already existing functionality. An important issue in the deployment of services is their run-time performance under various loads. Due to the complex interactions of the underlying services, a CWS they can exhibit problematic and often difficult to predict behaviours in overload situations. This paper focuses on the use of request scheduling for improving CWS performance in overload situations. Different scheduling policies are investigated in regards to their effectiveness in helping with bulk arrivals.

Multi-Channel Bi-Level Heterogeneous Servers Bulk Arrival Queueing System with Erlangian Service Time

An easily applicable algorithm to solve problems involving bulk-arrival queues with a breakdown of one of the heterogeneous servers in case of steady state is introduced. A Monte Carlo study for numerically finding the limiting distribution of the number in the system for the bulk arrival, multi-server queueing model (M[x]/EK/C; C-1/FCFS) with heterogeneous servers is presented. The system consists of servers of varying efficiency. This paper presents multi-channel queue with Poisson arrivals, Erlangian service time distributions in which all servers have equal breakdown chance. Measures of system performance including mean queue length, mean waiting time, and blocking probability are reported. Numerical results are obtained by simulation of the entire system. Examples of extensive numerical results for certain measures of efficiency are presented in tabular and chart form. In all cases, the proposed method is computationally efficient, accurate and reliable for both high and low values of the model parameters.

The processor-sharing queue with bulk arrivals and phase-type services

In this paper, we consider a queue with compound Poisson arrivals, phase type required service times in which a single processor serves according to the processor-sharing discipline. For this queue...

The processor-sharing queue with bulk arrivals and phase-type services

In this paper, we consider a queue with compound Poisson arrivals, phase type required service times in which a single processor serves according to the processor-sharing discipline. For this queue, we derive a system of equations for the transform of the queue-length and obtain the moments of the queue-length as a solution of linear equations. We also obtain a system of equations for the joint transforms of the sojourn time and the queue-length and find the moments of the sojourn time as a solution of linear equations. Numerical examples show that the smaller the variation of the required service times becomes, the larger the mean and variance of the sojourn times become.

Performance analysis of a finite-buffer discrete-time queue with bulk arrival, bulk service and vacations

This paper considers a finite-buffer discrete-time GeoX/GY/1/K+B queue with multiple vacations that has a wide range of applications including high-speed digital telecommunication systems and various related areas. The main purpose of this paper is to present a performance analysis of this system. For this purpose, we first derive a set of linear equations to compute the steady-state departure-epoch probabilities based on the embedded Markov chain technique. Next, we present numerically stable relationships for the steady-state probabilities of the queue lengths at three different epochs: departure, random, and arrival. Finally, based on these relationships, we present various useful performance measures of interest such as the moments of the number of packets in the queue at three different epochs, the mean delay in the queue of a packet, the loss probability and the probability that server is busy with computational experiences.

Computational Analysis of a Multi-Server Bulk Arrival with Two Modes Server Breakdown

An extensive Monte Carlo study is performed to analyze a multi-server, bulk arrival (M [x]M/C; C-1/FCFS) queuing system. The system breakdown limits the system to serve with either C or (C-1) servers. The server breakdown has equal chance over all servers in the system while the arrival process is a Poisson process and the distribution of the bulk size X is a positive Poisson bulk size. Measures of system efficiency including mean queue length, mean waiting time, and blocking probability are introduced. Numerical results are obtained by simulation of the entire system.

Worst closed-loop controlled bulk distributions of stochastic arrival processes for queue performance

This paper presents basic queueing analysis contributing to teletraffc theory, with commonly accessible mathematical tools. This paper studies queueing systems with bulk arrivals. It is assumed that the number of arrivals and the expected number of arrivals in each bulk are bounded by some constraints B and λ, respectively. Subject to these constraints, convexity argument is used to show that the bulk-size probability distribution that results in the worst mean queue performance is an extremal distribution with support {1, B} and mean equal to λ. Furthermore, from the viewpoint of security against denial-of-service attacks, this distribution remains the worst even if an adversary were allowed to choose the bulk-size distribution at each arrival instant as a function of past queue lengths; that is, the adversary can produce as bad queueing performance with an open-loop strategy as with any closed-loop strategy. These results are proven for an arbitrary arrival process with bulk arrivals and a general service model.

Performance analysis of a finite-buffer discrete-time queue with bulk arrival, bulk service and vacations

This paper considers a finite-buffer discrete-time Geo X / G Y /1/ K+ B queue with multiple vacations that has a wide range of applications including high-speed digital telecommunication systems and various related areas. The main purpose of this paper is to present a performance analysis of this system. For this purpose, we first derive a set of linear equations to compute the steady-state departure-epoch probabilities based on the embedded Markov chain technique. Next, we present numerically stable relationships for the steady-state probabilities of the queue lengths at three different epochs: departure, random, and arrival. Finally, based on these relationships, we present various useful performance measures of interest such as the moments of the number of packets in the queue at three different epochs, the mean delay in the queue of a packet, the loss probability and the probability that server is busy with computational experiences.

An algorithm for computing the mean response time of a single server queue with generalized on/off traffic arrivals

In this paper, an exact solution for the response time distribution of a single server, infinite capacity, discrete-time queue is presented. This queue is fed by a flexible discrete-time arrival process, which follows an on/off evolution. A workload variable is associated with each arrival instant, which may correspond to the service demand generated by a single arrival, or represent the number of simultaneous arrivals (bulk arrivals). Accordingly, the analysis focuses on two types of queues: (On/Off)/G/1 and (Batch-On/Off)/D/1. For both cases, a decomposition approach is carried out, which divides the problem into two contributions: the response time experienced by single bursts in isolation, and the increase on the response time caused by the unfinished work that propagates from burst to burst. Particularly, the solution for the unfinished work is derived from a Wiener-Hopf factorization of random walks, which was already used in the analysis of discrete GI/G/1 queues. Compared to other related works, the procedure proposed in this paper is exact, valid for any traffic intensity and has no constraints on the distributions of the input random variables characterizing the process: duration of on and off periods, and workload. From the general solution, an efficient and robust iterative algorithm for computing the expected response time of both queues is developed, which can provide results at any desired precision. This algorithm is numerically evaluated for different types of input distributions and proved against simulation.

Complete analytic and computational analyses of the discrete-time bulk-arrival infinite-server system: GIX/ Geom/∞

In this paper, we consider the discrete-time queueing system with bulk arrivals, generally distributed interbatch times, geometrically distributed service times, and infinite number of servers: the GI X / Geom/∞ queue. Under the assumptions of early arrival system (EAS) and late arrival system (LAS), we derive the system size distributions at two different epochs—prearrival and random. In addition, simple relations among the binomial moments of the steady-state system-size distributions of the two systems are derived. Special cases, such as the GI/ Geom/∞ or GI/ D/∞ queues, are also presented. Some numerical results are included at the end.

Analysis of the M/G/1 processor-sharing queue with bulk arrivals

We analyze the single server processor-sharing queue for the case of bulk arrivals. We obtain an expression for the expected response time of a job as a function of its size, when the service times of jobs have a generalized hyperexponential distribution and more generally for distributions with rational Laplace transforms. Our analysis significantly extends the class of distributions for which processor-sharing queues with bulk arrivals were previously analyzed.

A complete and simple solution for a discrete-time multi-server queue with bulk arrivals and deterministic service times

A complete distribution for the system content of a discrete-time multi-server queue with an infinite buffer is presented, where each customer arriving in a group requires a deterministic service time that could be greater than one slot. In addition, when the service time equals one slot, a complete distribution for the delay is also presented.

Analysis of Nonpreemptive Priority Queueing of DiffServ Networks with Bulk Arrivals

Abstract The queueing delay and packet loss performance of priority-based differentiated services (DiffServ) networks are analyzed through the nonpreemptive M/M/m/K finite queueing bulk arrival model. The analytical results reveal the queueing time relation of different priority classes of data traffic due to the differentiated services priority queueing and scheduling control network operations.

Marking Optimization of Weighted Marked Graphs

Cyclic manufacturing systems can be modeled by marked graphs, which are an elementary class of Petri nets. To model systems with bulk services and arrivals and to reduce the size of the model, weighted marked graphs can be used. An important step when designing these systems is the definition of the number of manufacturing resources to be used in order to reach a given productivity. In terms of timed Petri nets, this is known as the marking optimization problem and consists of reaching a given average cycle time while minimizing a linear combination of markings. In this paper, a necessary and sufficient condition to obtain a feasible solution of the marking optimization problem of weighted marked graphs with deterministic times is established. A fast heuristic solution, based on an iterative process and using simulation, is given. An example and an application to manufacturing systems are presented.