A Markovian queue with varying number of servers and applications to the performance comparison of HSDPA user equipment

Inspired by the need for performability models for HSDPA user equipment, a Markovian queue with varying number of servers is conceived. The arrival and the service processes, the number of allocated or active servers of the queue are inherently, and independently (or jointly) Markov modulated. Batch...

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Bibliographic Details
Published in:Acta informatica 2011-07, Vol.48 (4), p.243-269
Main Authors: Do, Tien Van, Chakka, Ram, Do, Nam H., Pap, László
Format: Article
Language:English
Subjects:
Applied sciences
Arrivals
Autocorrelation
Channels
Communication
Communications networks
Computer Science
Computer science
control theory
systems
Computer Systems Organization and Communication Networks
Customer services
Data Structures and Information Theory
Exact sciences and technology
Information Systems and Communication Service
Logics and Meanings of Programs
Markov analysis
Markov processes
Mathematical analysis
Mathematical models
Miscellaneous
Multiple births
Original Article
Queues
Queuing
Queuing theory
Servers
Software Engineering/Programming and Operating Systems
Studies
Theoretical computing
Theory of Computation
Wireless networks
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Summary:Inspired by the need for performability models for HSDPA user equipment, a Markovian queue with varying number of servers is conceived. The arrival and the service processes, the number of allocated or active servers of the queue are inherently, and independently (or jointly) Markov modulated. Batch arrivals, batch services, autocorrelation of inter-arrival times, and autocorrelation of batch sizes can be accommodated in the queue, by a suitable use of Markov modulation and generalized exponential distribution. The queue has a provision for negative customers too. Transformations of the balance equations into a computable form are proposed in order to obtain the steady state probabilities with the Spectral Expansion method. This queue is used to model the High Speed Downlink Packet Access (HSDPA) wireless networks. The model is an integrated one with respect to HSDPA, capable of accommodating many of the intricate aspects of HSDPA such as, channel allocation policy, loss of packets due to channel fading, bursty and correlated traffic. Good agreement is observed between the numerical results of the proposed analytical model and those of an independent simulator of real HSDPA and radio channel behaviors. The comparison of the terminal categories specified by the 3rd Generation Partnership Project (3GPP) is also presented.
ISSN:0001-5903
1432-0525
DOI:10.1007/s00236-011-0138-7