scholarly journals Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Andrzej Chydzinski ◽  
Blazej Adamczyk
Keyword(s):  
Batch Size ◽  
Buffer Size ◽  
Arrival Process ◽  
Time Interval ◽  
Finite Buffer ◽  
Finite Time Interval ◽  
Batch Arrivals ◽  
Batch Markovian Arrival Process ◽  
Buffer Overflows ◽  
Finite Buffer Queue

We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batch Markovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations of the dependence of the number of losses on the average batch size, buffer size, system load, autocorrelation structure, and time.

ADMISSION CONTROL WITH INCOMPLETE INFORMATION TO A FINITE BUFFER QUEUE

2006 ◽  
Vol 21 (1) ◽  
pp. 19-46 ◽  
Author(s):  
Dorothée Honhon ◽  
Sridhar Seshadri
Keyword(s):  
Admission Control ◽  
Partial Information ◽  
Control Policy ◽  
Arrival Process ◽  
Finite Buffer ◽  
Optimal Cost ◽  
State Aggregation ◽  
The Cost ◽  
Finite Buffer Queue

We consider the problem of admission control to a multiserver finite buffer queue under partial information. The controller cannot see the queue but is informed immediately if an admitted customer is lost due to buffer overflow. Turning away (i.e., blocking) customers is costly and so is losing an admitted customer. The latter cost is greater than that of blocking. The controller's objective is to minimize the average cost of blocking and rejection per incoming customer. Lin and Ross [11] studied this problem for multiserver loss systems. We extend their work by allowing a finite buffer and the arrival process to be of the renewal type. We propose a control policy based on a novel state aggregation approach that exploits the regenerative structure of the system, performs well, and gives a lower bound on the optimal cost. The control policy is inspired by a simulation technique that reduces the variance of the estimators by not simulating the customer service process. Numerical experiments show that our bound varies with the load offered to the system and is typically within 1% and 10% of the optimal cost. Also, our bound is tight in the important case when the cost of blocking is low compared to the cost of rejection and the load offered to the system is high. The quality of the bound degrades with the degree of state aggregation, but the computational effort is comparatively small. Moreover, the control policies that we obtain perform better compared to a heuristic suggested by Lin and Ross. The state aggregation technique developed in this article can be used more generally to solve problems in which the objective is to control the time to the end of a cycle and the quality of the information available to the controller degrades with the length of the cycle.

scholarly journals Analysis of Queue-Length Dependent Vacations and P-Limited Service in BMAP/G/1/N Systems: Stationary Distributions and Optimal Control

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
A. D. Banik
Keyword(s):  
Queue Length ◽  
Minimum Cost ◽  
Arrival Process ◽  
Service Discipline ◽  
Single Server ◽  
Finite Buffer ◽  
Batch Markovian Arrival Process ◽  
Special Cases ◽  
Number Of Customers ◽  
Limited Service

We consider a finite-buffer single server queueing system with queue-length dependent vacations where arrivals occur according to a batch Markovian arrival process (BMAP). The service discipline is P-limited service, also called E-limited with limit variation (ELV) where the server serves until either the system is emptied or a randomly chosen limit of L customers has been served. Depending on the number of customers present in the system, the server will monitor his vacation times. Queue-length distributions at various epochs such as before, arrival, arbitrary and after, departure have been obtained. Several other service disciplines like Bernoulli scheduling, nonexhaustive service, and E-limited service can be treated as special cases of the P-limited service. Finally, the total expected cost function per unit time is considered to determine locally optimal values N* of N or a maximum limit L^* of L^ as the number of customers served during a service period at a minimum cost.

scholarly journals Poisson traffic flow in a general feedback queue

2002 ◽  
Vol 39 (03) ◽  
pp. 630-636 ◽  
Author(s):  
Erol A. Peköz ◽  
Nitindra Joglekar
Keyword(s):  
Arrival Process ◽  
Finite Buffer ◽  
Feedback Delay ◽  
Highway Traffic ◽  
Customer Feedback ◽  
Mild Conditions ◽  
Continuous Density ◽  
Poisson Arrivals ◽  
Finite Buffer Queue ◽  
Feedback Queue

Consider a ·/G/kfinite-buffer queue with a stationary ergodic arrival process and delayed customer feedback, where customers after service may repeatedly return to the back of the queue after an independent general feedback delay whose distribution has a continuous density function. We use coupling methods to show that, under some mild conditions, the feedback flow of customers returning to the back of the queue converges to a Poisson process as the feedback delay distribution is scaled up. This allows for easy waiting-time approximations in the setting of Poisson arrivals, and also gives a new coupling proof of a classic highway traffic result of Breiman (1963). We also consider the case of nonindependent feedback delays.

scholarly journals Voltage Control-Based Ancillary Service Using Deep Reinforcement Learning

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2274
Author(s):  
Oleh Lukianykhin ◽  
Tetiana Bogodorova
Keyword(s):  
Reinforcement Learning ◽  
Voltage Control ◽  
Batch Size ◽  
Buffer Size ◽  
Time Interval ◽  
State Variables ◽  
Ancillary Service ◽  
Model Free ◽  
Thermostatically Controlled Loads ◽  
Hidden Layer

Ancillary services rely on operating reserves to support an uninterrupted electricity supply that meets demand. One of the hidden reserves of the grid is in thermostatically controlled loads. To efficiently exploit these reserves, a new realization of control of voltage in the allowable range to follow the set power reference is proposed. The proposed approach is based on the deep reinforcement learning (RL) algorithm. Double DQN is utilized because of the proven state-of-the-art level of performance in complex control tasks, native handling of continuous environment state variables, and model-free application of the trained DDQN to the real grid. To evaluate the deep RL control performance, the proposed method was compared with a classic proportional control of the voltage change according to the power reference setup. The solution was validated in setups with a different number of thermostatically controlled loads (TCLs) in a feeder to show its generalization capabilities. In this article, the particularities of deep reinforcement learning application in the power system domain are discussed along with the results achieved by such an RL-powered demand response solution. The tuning of hyperparameters for the RL algorithm was performed to achieve the best performance of the double deep Q-network (DDQN) algorithm. In particular, the influence of a learning rate, a target network update step, network hidden layer size, batch size, and replay buffer size were assessed. The achieved performance is roughly two times better than the competing approach of optimal control selection within the considered time interval of the simulation. The decrease in deviation of the actual power consumption from the reference power profile is demonstrated. The benefit in costs is estimated for the presented voltage control-based ancillary service to show the potential impact.

scholarly journals On the Queue Length Distribution in BMAP Systems

2017 ◽  
Vol 2 (4) ◽  
pp. 275 ◽  
Author(s):  
Andrzej Chydzinski
Keyword(s):  
Poisson Process ◽  
Queue Length ◽  
Length Distribution ◽  
Compound Poisson Process ◽  
Arrival Process ◽  
Finite Buffer ◽  
Batch Markovian Arrival Process ◽  
Queue Length Distribution ◽  
Markovian Processes ◽  
The Laplace Transform

Batch Markovian Arrival Process – BMAP – is a teletraffic model which combines high ability to imitate complexstatistical behaviour of network traces with relative simplicity in analysis and simulation. It is also a generalization of a wide class of Markovian processes, a class which in particular include the Poisson process, the compound Poisson process, the Markovmodulated Poisson process, the phase-type renewal process and others. In this paper we study the main queueing performance characteristic of a finite-buffer queue fed by the BMAP, namely the queue length distribution. In particular, we show a formula for the Laplace transform of the queue length distribution. The main benefit of this formula is that it may be used to obtain both transient and stationary characteristics. To demonstrate this, several numerical results are presented.

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