Heavy traffic limits in a wireless queueing model with long range dependence

Buche, R.; Ghosh, Arka P.; Pipiras, Vladas

doi:10.1109/cdc.2007.4434727

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…The relationship is illustrated, in particular, for the infinite source Poisson arrival model where surprisingly simple relationship among heavy tail exponent α, source rate λ and variation parameter ν is obtained for various (namely, sLm, fBm or Bm) limits. When the function u (x, j) above does not depend on j, similar conditions were derived in Buche, Ghosh and Pipiras (2007).…”

Section: Introductionmentioning

confidence: 79%

Heavy Traffic Approximations of a Queue with Varying Service Rates and General Arrivals

2012

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Heavy traffic limit theorems are established for a class of single server queueing models including those with heavy-tailed or long-range dependent arrivals and time-varying service rates. The models are motivated by wireless queueing systems for which there is an increasing evidence of the presence of heavy-tailed or long range dependent arrivals, and where the service rates vary with the changes in the wireless medium. Since changes in the wireless medium occur slowly, the service rate is assumed to vary slower than that of the arrivals.The main focus of the paper is to obtain the different possible limit forms that can arise depending on the relationship between established scalings for both the arrival and departure processes. The limit forms obtained here are driven by either Brownian motion (when the contribution from the departure process dominates the limit) or the limits of properly scaled arrivals (when the contribution from the arrival process dominates the limit), typical examples being stable Lévy motion or fractional Brownian motion. In particular, for the case where arrival process is given by the infinite source Poisson process, this relationship, which determines the type of the limiting queue-length process, is a simple condition involving the heavy tail exponent, arrival rate and channel variation parameter in the wireless medium model. The limit forms are also affected by the assumption of a slower varying service rate.To establish these limit results, two approaches are studied. In one approach, when the limit is driven by Brownian motion, the perturbed test function method is extended to incorporate reflection. In contrast, the second approach allows for non-Markovian driving processes in the limit. Both approaches involve averaging in the drift term arising from random service rates at the departures. In the second approach, this averaging is carried out directly and pathwise, thus sidestepping the assumption of driving Brownian motion used in the perturbed test function method. In the case of the infinite source Poisson model, when the limit is stable Lévy motion, it is also argued how the limit form can be deduced using infinitesimal operators.

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Section: Introductionmentioning

confidence: 79%

Heavy Traffic Approximations of a Queue with Varying Service Rates and General Arrivals

2012

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“…That is, when the traffic intensity of the server approaches 1 and the system is operating at near capacity. Even when the system has a moderate traffic, the insights provided by heavy traffic analysis is very interesting from operator visions; see [9]. For heavy traffic analysis we form a sequence of queuing systems indexed by n ¼ 1; 2; .…”

Section: Heavy Traffic Analysis For Modellingmentioning

confidence: 99%

Optimal scheduling and power allocation in wireless networks with heavy traffic

Baili

Assaad

2015

Mathematical and Computer Modelling of Dynamical Systems

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This paper addresses the problem of joint transmit power allocation and time slot scheduling in a wireless communication system with time varying traffic. The system is handled by a single base station transmitting over time varying channels. This may be the case in practice of a hybrid TDMA-CDMA (Time Division Multiple AccessCode Division Multiple Access) system. The operating time horizon is divided into time slots; a fixed amount of power is available at each time slot. The users share each time slot and the power available at this time slot with the objective of minimizing the expected total queue length. The problem is reformulated, via a heavy traffic approximation, as the optimal control of a reflected diffusion in the positive orthant. We establish a closed form solution for the obtained control problem. The main feature that makes it possible is an astute choice of some auxiliary weighting matrices in the cost rate. The proposed solution relies also on the knowledge of the covariance matrix of the non-standard multi-dimensional Wiener process which is the driving process in the reflected diffusion. We then compute this covariance matrix given the stationary distribution of the multi-dimensional channel process. Further stochastic analysis is provided: the cost variance, and the Fokker-Planck equation for the distribution density of the queue length.

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Congestion Control in Distributed Networks - A Comparative Study

Vinodha

Selvarani²

2012

Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Heavy traffic limits in a wireless queueing model with long range dependence

Cited by 3 publications

References 18 publications

Heavy Traffic Approximations of a Queue with Varying Service Rates and General Arrivals

Heavy Traffic Approximations of a Queue with Varying Service Rates and General Arrivals

Optimal scheduling and power allocation in wireless networks with heavy traffic

Congestion Control in Distributed Networks - A Comparative Study

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