Two classes of time-inhomogeneous Markov chains: Analysis of the periodic case

Alfa, Attahiru Sule; Margolius, Barbara

doi:10.1007/s10479-007-0300-3

Cited by 11 publications

(6 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bookbinder and Martell [22] minimize the damage potential of forest fires by considering the allocation of available helicopters. Alfa and Margolius [11] evaluate the queue of requests for police patrol cars, and Kolesar et al [130] and Ingolfsson et al [103] apply time-dependent queueing systems as part of scheduling algorithms for police patrol cars.…”

Section: Service Systemsmentioning

confidence: 99%

“…Collings and Stoneman [42] EXPL Agnihothri and Taylor [3] x x SIPP Brahimi and Worthington [23] x D T A Bennett and Worthington [16] x D T A de Bruin et al [54] x SIPP Singer and Donoso [199] x SIPP Gillard and Knight [78] x CKE Vanberkel et al [222] x x PSA Yom-Tov and Mandelbaum [239] x x MOL Emergency services Kolesar et al [130] x x CKE, SIPP Bookbinder and Martell [22] x x CKE Green and Kolesar [84] SPHA Ingolfsson et al [103] x x CKE, SIPP Green et al [91] x x SIPP Alfa and Margolius [11] x D T A…”

Section: Health Carementioning

confidence: 99%

See 1 more Smart Citation

Performance Analysis of Time-Dependent Queueing Systems: Survey and Classification

2015

View full text Add to dashboard Cite

Section: Service Systemsmentioning

confidence: 99%

Section: Health Carementioning

confidence: 99%

Performance Analysis of Time-Dependent Queueing Systems: Survey and Classification

2015

View full text Add to dashboard Cite

“…As noted by Margolius [41], computational methods and approximation techniques involved in time-varying queueing problems have long been regarded as challenging. The time-varying ingredients can exist in the arrival processes, service durations, or the number of servers, as mentioned by Alfa and Margolius [4].…”

Section: Time-varying Queuesmentioning

confidence: 99%

“…4, we continue to analyze the upper bound of carryover probability specified in inequality (4.10). As for E − j , j = 1, 2, .…”

Section: and Pr(nmentioning

confidence: 99%

Perfect and nearly perfect sampling of work-conserving queues

2015

View full text Add to dashboard Cite

We present sampling-based methods to treat work-conserving queueing systems. A variety of models are studied. Besides the First Come First Served (FCFS) queues, many efforts are putted on the accumulating priority queue (APQ), where a customer accumulates priority linearly while waiting. APQs have Poisson arrivals, multi-class customers with corresponding service durations, and single or multiple servers.Perfect sampling is an approach to draw a sample directly from the steady-state distribution of a Markov chain without explicitly solving for it. Statistical inference can be conducted without initialization bias. If an error can be tolerated within some limit, i.e. the total variation distance between the simulated draw and the stationary distribution can be bounded by a specified number, then we get a so called "nearly" perfect sampling.Coupling from the past (CFTP) is one approach to perfect sampling, but it usually requires a bounded state space. One strategy for perfect sampling on unbounded state spaces relies on construction of a reversible dominating process. If only the dominating property is guaranteed, then regenerative method (RM) becomes an alternative choice. In the case where neither the reversibility nor dominance hold, a nearly perfect sampling method will be proposed. It is a variant of dominated CFTP that we call the CFTP Block Absorption (CFTP-BA) method.Time-varying queues with periodic Poisson arrivals are being considered in this thesis. It has been shown that a particular limiting distribution can be obtained for each point in time in the periodic cycle. Because there are no analytical solutions in closed forms, we explore perfect (or nearly perfect) sampling of these systems.

show abstract

“…, A k }. Such chains arise in diverse settings including flocking [20], simulated annealing in optimization [4], Monte Carlo methods [22] and queueing theory [2].…”

Section: Introductionmentioning

confidence: 99%

Sets of Stochastic Matrices with Converging Products: Bounds and Complexity

Chevalier¹,

Gusev²,

Jungers³

et al. 2017

Preprint

View full text Add to dashboard Cite

An SIA matrix is a stochastic matrix whose sequence of powers converges to a rank-one matrix. This convergence is desirable in various applications making use of stochastic matrices, such as consensus, distributed optimization and Markov chains. We study the shortest SIA products of sets of matrices. We observe that the shortest SIA product of a set of matrices is usually very short and we provide a first upper bound on the length of the shortest SIA product (if one exists) of any set of stochastic matrices. We also provide an algorithm that decides the existence of an SIA product.When particularized to automata, the problem becomes that of finding periodic synchronizing words, and we develop the consequences of our results in relation with the celebrated Černý conjecture in automata theory.We also investigate links with the related notions of positive-column, Sarymsakov, and scrambling matrices.

show abstract

Two classes of time-inhomogeneous Markov chains: Analysis of the periodic case

Cited by 11 publications

References 8 publications

Performance Analysis of Time-Dependent Queueing Systems: Survey and Classification

Performance Analysis of Time-Dependent Queueing Systems: Survey and Classification

Perfect and nearly perfect sampling of work-conserving queues

Sets of Stochastic Matrices with Converging Products: Bounds and Complexity

Contact Info

Product

Resources

About