A discrete-time Markov modulated queuing system with batched arrivals

This paper examines a discrete-time queuing system with applications to telecommunications traffic. The arrival process is a particular Markov modulated process which belongs to the class of discrete batched Markovian arrival processes. The server process is a single server deterministic queue. A closed form exact solution is given for the expected queue length and delay. A simple system of equations is given for the probability of the queue exceeding a given length.Comment: to appear Performance Evaluatio

Analysis and Computation of the Joint Queue Length Distribution in a FIFO Single-Server Queue with Multiple Batch Markovian Arrival Streams

This paper considers a work-conserving FIFO single-server queue with multiple batch Markovian arrival streams governed by a continuous-time finite-state Markov chain. A particular feature of this queue is that service time distributions of customers may be different for different arrival streams. After briefly discussing the actual waiting time distributions of customers from respective arrival streams, we derive a formula for the vector generating function of the time-average joint queue length distribution in terms of the virtual waiting time distribution. Further assuming the discrete phase-type batch size distributions, we develop a numerically feasible procedure to compute the joint queue length distribution. Some numerical examples are provided also

An analysis of a batch server with variable and class-dependent service capacity

In many studies on batch service queueing systems, the service capacity is assumed to be constant. However, this service capacity often depends on the content of the queue. In this paper, we analyse a discrete-time single server batch server queue with general inde- pendent arrivals. We distinguish two dierent classes in the arrival stream and products of both classes are added to the tail of a single queue. The single batch server can group all waiting customers at the head of the queue that belong to the same product class up to a certain class-dependent maximum capacity. This results in a stochastic service capacity that depends on both the number of customers in the queue and their respective classes. Since it is clear that the length of a sequence of same-class customers will have a signicant impact on the performance of the system, we also include correlation between the classes of consecutive customers. Applications of this type of batch server can, for instance, be found in the pacemaker loop of a Lean manufacturing system. In the course of the analysis, we calculate the probability generating function of the system occupancy at service initi- ation opportunities. In the numerical experiments, we will look at the impact of dierent parameters on both the mean system occupancy and the probability that the server is idle at a random service initiation opportunity. We also provide a number of guidelines to pick between the exact solution and an approximated approach with unlimited service capacities, by looking at the trade-o between accuracy and computational complexity

Queues with Galton-Watson-type arrivals

This paper presents the analysis of a discrete-time single server queueing system with a multi-type Galton-Watson arrival process with migration. It is shown that such a process allows to capture intricate correlation in the arrival process while the corcesponding queueing analysis yields closed-form expressions for various moments of queue content and packet delay

Fixed points for multi-class queues

Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result to multi-type queues, in which different types of customer have different levels of priority. We work with a model of a queueing server which includes discrete-time and continuous-time M/M/1 queues as well as queues with exponential or geometric service batches occurring in discrete time or at points of a Poisson process. The fixed-point results are proved using interchangeability properties for queues in tandem, which have previously been established for one-type M/M/1 systems. Some of the fixed-point results have previously been derived as a consequence of the construction of stationary distributions for multi-type interacting particle systems, and we explain the links between the two frameworks. The fixed points have interesting "clustering" properties for lower-priority customers. An extreme case is an example of a Brownian queue, in which lower-priority work only occurs at a set of times of measure 0 (and corresponds to a local time process for the queue-length process of higher priority work).Comment: 25 page

Discrete-time queues with zero-regenerative arrivals: moments and examples

In this paper we investigate a single-server discrete-time queueing system with single-slot service times. The stationary ergodic arrival process this queueing system is subject to, satisfies a regeneration property when there are no arrivals during a slot. Expressions for the mean and the variance of the queue content in steady state are obtained for this broad class which includes among others autoregressive arrival processes and M/G/infinity-input or train arrival processes. To illustrate our results, we then consider a number of numerical examples

The NxD-BMAP/G/1 queueing model : queue contents and delay analysis

We consider a single-server discrete-time queueing system with N sources, where each source is modelled as a correlated Markovian customer arrival process, and the customer service times are generally distributed. We focus on the analysis of the number of customers in the queue, the amount of work in the queue, and the customer delay. For each of these quantities, we will derive an expression for their steady-state probability generating function, and from these results, we derive closed-form expressions for key performance measures such as their mean value, variance, and tail distribution. A lot of emphasis is put on finding closed-form expressions for these quantities that reduce all numerical calculations to an absolute minimum

Pemodelan Simulasi Antrian dengan Metode Discrete Event Simulation Queue Simulation Modeling with Discrete Event Simulation Method

ABSTRAKSI: Pemodelan adalah suatu representasi sistem nyata dari objek-objek dengan mengambil bentuk matematis dan suatu relasi logika. Secara umum, simulasi didefinisikan sebagai representasi dinamis dari sebagian dunia nyata dengan menggunakan komputer dan berjalan berdasarkan waktu tertentu. Salah satu teknik pemodelan adalah Discrete Event Simulation (DES), melakukan pemodelan suatu sistem yang berubah setiap satuan waktu. Metode ini bersifat stochastic, dynamic, dan discret-event.Dalam tugas akhir ini diimplementasikan beberapa model simulasi antrian yang menggunakan aturan antrian yang berbeda-beda pada tiap model antrian. Model simulasi antrian yang dibangun adalah single server queue, multi server queue, time shared computer model, multi teller bank with jockeying, dan job-shop model.Model yang dihasilkan memiliki parameter customer, arrival dan service time. Dengan menghasilkan output waktu rata-rata dari jumlah total customer atau job dalam antrian, waktu rata-rata utilisasi server, waktu tunggu rata-rata customer sebelum dilayani oleh server. Hasil pengujian terhadap fungsionalitas aplikasi menunjukkan bahwa fungsi-fungsi dari model antrian dapat berjalan sesuai dengan spesifikasi yang telah ditetapkan.Kata Kunci : DES, antrian, state, event, model, simulasi.ABSTRACT: Modeling is a real system representation of objects with mathematical form and a logic relationship. In general, simulation defined as dynamic representation from some of real worlds by using computer and run with selected time. One of modeling technique is Discrete Event Simulation (DES), doing a system modeling what changing each everytime. This method have the character of stochastic, dynamic, and discrete-event.In this final exam implementation some queue simulation models using queue rule which different each other queue model. Queue simulation models the build are single server queue, multi server queue, time shared computer model, multi teller bank with jockeying, dan job-shop model.The model have parameter customer, arrival dan service time. With result output time average size of the queue, time average utilization of the Server, time average wait in queue. Examination result to application functionality indicate that functions of queue model can run and match with specification have been specified.Keyword: DES, queue, state, event, modeling, simulatio