Queueing Networks and Markov Chains

Bolch, Gunter; Greiner, Stefan; Meer, Hermann de; Trivedi, Kishor S.

doi:10.1002/0471200581

Cited by 591 publications

(265 citation statements)

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“…The astute reader may notice that this method bears a loose resemblance to the well-known uniformization technique [6][7][8] which can be used to generate transient-state distributions and passage time densities for Markov chains. However, as we are working with semi-Markov systems, there can be no uniformizing of the general distributions in the SMP.…”

Section: Iterative Transient Methodsmentioning

confidence: 99%

Distributed computation of transient state distributions and passage time quantiles in large semi-Markov models

Bradley

Dingle

Harrison

et al. 2006

Future Generation Computer Systems

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Section: Iterative Transient Methodsmentioning

confidence: 99%

Distributed computation of transient state distributions and passage time quantiles in large semi-Markov models

Bradley

Dingle

Harrison

et al. 2006

Future Generation Computer Systems

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“…The Markov chain would then be transformed into a system of linear equations (usually represented by a highly sparse matrix) reflecting the steady-state [5] . However, by using appropriate sparse representations and specialpurpose sparse solvers, this can be reduced significantly.…”

Section: General Solutionmentioning

confidence: 99%

“…Hence the exact solution of N G is determined by (5). The corresponding transition rates from an arbitrary state ) (g to possible successor states can also be derived as …”

Section: Solution By Exact Aggregationmentioning

confidence: 99%

“…Analytical models often are based on steadystate analysis of Markov chains, queuing networks [5] or Petri nets [1], the two latter ones usually being again mapped on Markov chains. The drawbacks of these approaches often include unrealistic assumptions on the observed traffic and the often observed explosion of the Markov chain state space.…”

Section: Introductionmentioning

confidence: 99%

“…There are several ways for reducing the state space of large Markov chains, for example by reducing the model complexity, analyzing the structure of the Markov chain generator matrix [7] or aggregating closely related states into one macro-state [5,8]. Depending on whether the Markov chain is exactly, ordinarily, or nearly lumpable, these aggregation techniques will yield exact solutions (for the whole chain or only the aggregated chain) or only approximations [9,6].…”

Section: Introductionmentioning

confidence: 99%

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Modelling resource management for multi-class traffic in mobile cellular networks

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Proceedings of the 35th Annual Hawaii International Conference on System Sciences

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Future cellular mobile networks will be limited by the number of channels available in each cell. On the other hand, new broadband applications like video telephony will demand tight quality of service guarantees that must be met by the network at all times. Thus, advanced mechanisms for allocating these channels to incoming calls with different quality of service level will be of utmost importance. In this paper we introduce a new analytical model for cell channel allocation to multiclass traffic. Being based on Markov chains, the new model exploits the multi-class property and reduces the state space dramatically, thus enabling the solution of previously unsolvable problem classes. We additionally describe CECALL, a simulator implementing several different strategies for allocating cell channels to multiclass traffic, handoff pre-reservation and degradation of low-level call classes. The results of the analytical model are used for explaining important simulation results.

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Determining the optimal inspection rate of circuit breakers equipped with condition monitoring devices using new maintenance Markov model

Karimabadi

Hajiabadi

Kamyab³

et al. 2020

Int Trans Electr Energ Syst

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Nowadays, the maintenance scheduling of equipment has been highly improved using condition monitoring (CM) systems. This paper determines the optimal inspection rate of circuit breakers equipped with CM using a novel mathematical procedure. To achieve this goal, in the first step, it is necessary to quantify the effect of CM on the early detection of minor failures of the equipment. Therefore, a mathematical formulation is provided to categorize and model the failures of the equipment based on their severity. Moreover, a new concept termed predictive maintenance (PDM) rate will be introduced and formulated in this paper. The PDM rate is applied in the maintenance process as the smart inspection rate of the equipment. In the second step, this paper proposes a new combined preventive and predictive maintenance Markov model. By developing the formulation of the proposed Markov model, an optimization problem is formed. In this optimization problem, the annual maintenance cost serves as the objective function and the inspection rates represent the decision variables. The comprehensive statistical study on the failures of 400kv‐CB of KREC in Iran and the implementation of the proposed method indicates that the CM and optimal inspection of the CB not only enhances the lifetime of the CB by 19.48 years but also lower the annual maintenance cost by 19%.

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Queueing Networks and Markov Chains

Cited by 591 publications

References 0 publications

Distributed computation of transient state distributions and passage time quantiles in large semi-Markov models

Distributed computation of transient state distributions and passage time quantiles in large semi-Markov models

Modelling resource management for multi-class traffic in mobile cellular networks

Determining the optimal inspection rate of circuit breakers equipped with condition monitoring devices using new maintenance Markov model

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