Performance analysis of a statistical multiplexer with control on input and/or service processes

Yamada, Hiroshi; Machihara, Fumiaki

doi:10.1016/0166-5316(92)90018-c

Cited by 20 publications

(7 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The steady-state probability, p ij , for X i, j is written as p ij : Prob{X i,j} p ij can be represented using the parameters O g , O off , P g , and P off via the procedure shown in the Appendix, based on the Markov state-transition diagram (Fig. 5) [6,7].…”

Section: State Probability In the Steady Statementioning

confidence: 99%

Performance evaluation of telecommunication systems with forcible cutoff control scheme

Kawata

Yamada

Horiguchi

et al. 2000

Electron. Comm. Jpn. Pt. I

Self Cite

View full text Add to dashboard Cite

The rapid growth of computer‐communication services means that telephone‐conversation traffic must compete for system resources with computer‐communication traffic carried by dial‐up connections to the Internet or intranets over public telephone switching networks. The traffic characteristics differ for the two types of service; for example, the mean holding time and peak traffic periods are different. However, because dial‐up connection calls occupy circuit lines for a long time, the grade of service (GoS) of telephone‐conversation calls may deteriorate during periods of peak demand. Another problem is that since a telephone switching network is dimensioned to satisfy the required GoS for telephone calls during peak demand periods, there will be surplus resources, and a significant opportunity cost, during off‐peak periods. One way to efficiently use these surplus switching‐network resources is to offer fixed‐cost best‐effort dial‐up connection service during off‐peak periods for telephone traffic. This also makes the demand for dial‐up connections less likely to affect the GoS of telephone‐conversation calls during peak periods. We propose a priority control scheme for such an off‐peak service. This scheme works as follows in a telephone switching system where both high‐priority telephone‐conversation calls and low‐priority dial‐up connection calls are offered. When a call arrives at the system and there are adequate resources available for an ordinary telephone‐conversation call, a high‐priority telephone call or a low‐priority dial‐up connection call can be connected. However, if a high‐priority call arrives at the system and there are not enough resources available to allow connection, an already connected dial‐up connection call is forcibly cut off to enable connection of the high‐priority telephone call, and thus guarantee the GoS of telephone calls. We evaluate the performance of a telecommunication system based on this scheme by using a Markov model. We derive the call‐blocking probabilities for both call types and the ratio of the amount of traffic that is forcibly cut off to the amount of offered traffic in the system, and show calculated results. We also discuss some guidelines for offering services using this scheme. © 2000 Scripta Technica, Electron Comm Jpn Pt 1, 83(6): 78–87, 2000

show abstract

Section: State Probability In the Steady Statementioning

confidence: 99%

Performance evaluation of telecommunication systems with forcible cutoff control scheme

Kawata

Yamada

Horiguchi

et al. 2000

Electron. Comm. Jpn. Pt. I

Self Cite

View full text Add to dashboard Cite

show abstract

“…A close observation of (17) indicates that the major portion of the workload at the i-th step is made up by the following block operations:…”

Section: ~( ' + 1 ) = -~( I )~( I ) -'~( I ) mentioning

confidence: 99%

“…The other five basic blocks in (27) are updated by the basic update formulae of (17). If Pi is still odd-sized, repeat the above reduction step until the reduced matrix becomes even-sized.…”

Section: E Extension: Arbitrary Buffer Sitementioning

confidence: 99%

Folding algorithm: a computational method for finite QBD processes with level-dependent transitions

Li²

1994

IEEE Trans. Commun.

View full text Add to dashboard Cite

Absttact-This paper presents a new computational method for steady state analysis of finite QBD-process with leveldependent transitions. The QBD state space is defined in two-dimension with N phases and K levels. Instead of formulating solutions in matrix-geometric form, the Foldingalgorithm provides a technique for direct computation of aP = 0, where P is the QBD generator which is an ( N K ) x (NK) matrix. Taking a finite sequence of fixed-cost binary reduction steps, the K-level matrix P is eventually reduced to a single-level matrix, from which a boundary vector is obtained. Each step halves the matrix size but keeps the QBD form. The solution T is expressed as a product of the boundary vector and a finite sequence of expansion fac- tors. The time and space comp'exity for solving aP = o is therefore reduced from O ( N 3 K ) and O(N'K) to O(N310ga K )and O ( N a log, A'), respectively. The Folding-algorithm has a number of highly desirable advantages when it is applied to queueing analysis. First, the algorithm handles the multilevel control problem in finite buffer systems. Second, its total independence of the phase structure allows the algorithm to apply to more elaborate, multiple-state Markovian sources. Its computational efficiency, numerical stability and superior error performance are also distinctive advantages.algorithm, for direct computation of T P = 0, where T is the equilibrium solution vector. The Folding-algoritlhm is developed on the basis of Markov chain reduction. I t exploits the QBD structure to diminish large level-induced complexity. The time and space complexity of the Foldingalgorithm to solve TP = 0 is equal to O ( N 3 log, K ) and O ( N 2 log, K), respectively. In contrast, a direct application of the block Gaussian elimination (or block LU decomposition) will yield a time and space complexity of O ( N 3 K ) and O ( N 2 K ) [9]. applications in telecommunication network research. Typically, one can use a finite QBD-process with level-dependent transitions to model a statistical multiplexer with finite buffer and Markov chain modulated input, subject to input rate regulation, buffer overload control and dynamic link capacity allocation. Its state space, K x N , in reality may well exceed lo6 in size. This is because the number of levels ( I O , or the buffer size, can be up to around lo3; at about the same order of magnitude is the number of phases ( N ) at each level, which is the size of input Markov chain for aggregate multimedia traffic. For practical purposes, the time complexity by Folding-algorithm is only O ( N 3 ) .This moderate complexity makes implementation on small computers feasible. Since this paper focuses on the dgorithm, only a few representative examples are selected to demonstrate the stability, accuracy and efficiency of the al- gorithm. Extensive numerical studies can be found in [lo,The paper is organized as follows. Section I1 describes the algorithm. Section I11 gives the time and space complexity, and error characteristics. Section IV shows the application to...

show abstract

“…In [ll] and [15], Maglaris and his colleagues approximate the arrival stream of encoded video sequences to a multiplexer by an MMPP where the underlying Markov chain is a birth-death process. Saito, Kawarasaki and Yamada [14] as the traffic source model to analyze an ATM transport network and Yamada and Machiliara [19] investigate control methods of a ~tat~istical multiplexer with MMPP input streams.…”

Section: Introductionmentioning

confidence: 99%

Cyclic markov modulated poisson processes in traffic characterization

Chen

Rieders²

1996

Communications in Statistics. Stochastic Models

View full text Add to dashboard Cite

A new class of Markov modulated Poisson processes (MhIPP) is introduced where arrival rates vary according to a cyclic Markov chain. A closed form expression for the autocovariance function of the arrival rate process is derived and a recursive procedure for its calculation is given. Using a least square fitting procedure, the cyclic MMPP is applied to model packetized video traffic. A comparison with simulation results and other MMPP models from the literature reveal that a cyclic model can provide good est,imates for performance measures of interest.

show abstract

Performance analysis of a statistical multiplexer with control on input and/or service processes

Cited by 20 publications

References 14 publications

Performance evaluation of telecommunication systems with forcible cutoff control scheme

Performance evaluation of telecommunication systems with forcible cutoff control scheme

Folding algorithm: a computational method for finite QBD processes with level-dependent transitions

Cyclic markov modulated poisson processes in traffic characterization

Contact Info

Product

Resources

About