Performance analysis of time-dependent queueing systems: Survey and classification

Schwarz, Justus Arne; Selinka, Gregor; Stolletz, Raik

doi:10.1016/j.omega.2015.10.013

Cited by 80 publications

(25 citation statements)

References 214 publications

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“…This average number of vehicles is the maximal average number of vehicles k max in (2) achieved in the queueing system for the given values of λ, µ, and p. It is obvious that when pλ = µ, the average number of vehicles diverges, and under the stability condition µ ≥ pλ, the system does not fulfill its objective (26). This queueing system is the usual state in practical conditions.…”

Section: Solving Queueing Systems With Only An Infinite-capacity Sharmentioning

confidence: 96%

“…This attitude has somewhat discouraged further efforts in the analytical approach of the queuing theory and was consistently described by Koenigsberg in the set and reasoned antithesis [25]. His absolutely correct assessment of the necessity of analytical approach and positive development prognosis, confirmed Schwartz, Selinka and Stoletz, especially for non-stationary time-dependent non-Markovian queuing systems [26]. The analytical approach to solving the queuing system remains an imperative.…”

Section: Queueing System Phenomenonmentioning

confidence: 99%

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New Analytic Solutions of Queueing System for Shared–Short Lanes at Unsignalized Intersections

et al. 2019

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Designing the crossroads capacity is a prerequisite for achieving a high level of service with the same sustainability in stochastic traffic flow. Also, modeling of crossroad capacity can influence on balancing (symmetry) of traffic flow. Loss of priority in a left turn and optimal dimensioning of shared-short line is one of the permanent problems at intersections. A shared–short lane for taking a left turn from a priority direction at unsignalized intersections with a homogenous traffic flow and heterogeneous demands is a two-phase queueing system requiring a first in–first out (FIFO) service discipline and single-server service facility. The first phase (short lane) of the system is the queueing system M(pλ)/M(μ)/1/∞, whereas the second phase (shared lane) is a system with a binomial distribution service. In this research, we explicitly derive the probability of the state of a queueing system with a short lane of a finite capacity for taking a left turn and shared lane of infinite capacity. The presented formulas are under the presumption that the system is Markovian, i.e., the vehicle arrivals in both the minor and major streams are distributed according to the Poisson law, and that the service of the vehicles is exponentially distributed. Complex recursive operations in the two-phase queueing system are explained and solved in manuscript.

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Section: Solving Queueing Systems With Only An Infinite-capacity Sharmentioning

confidence: 96%

Section: Queueing System Phenomenonmentioning

confidence: 99%

New Analytic Solutions of Queueing System for Shared–Short Lanes at Unsignalized Intersections

et al. 2019

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“…Let us start with describing the behavior of an individual customer. After arrival at moment t 0 , a customer may (1) receives service immediately, (2) stand at the end of the queue.…”

Section: The Process Associating With An Individual Customermentioning

confidence: 99%

“…Recently, there has been an increasing interest in studying queueing systems when all the parameters are varying in time; see, for instance, [1]. This is due to the fact that these types of systems are more realistic and the periodic behavior of our daily live in different fields can be treated as well.…”

Section: Introductionmentioning

confidence: 99%

On Probability Characteristics for a Class of Queueing Models with Impatient Customers

et al. 2020

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In this paper, a class of queueing models with impatient customers is considered. It deals with the probability characteristics of an individual customer in a non-stationary Markovian queue with impatient customers, the stationary analogue of which was studied previously as a successful approximation of a more general non-Markov model. A new mathematical model of the process is considered that describes the behavior of an individual requirement in the queue of requirements. This can be applied both in the stationary and non-stationary cases. Based on the proposed model, a methodology has been developed for calculating the system characteristics both in the case of the existence of a stationary solution and in the case of the existence of a periodic solution for the corresponding forward Kolmogorov system. Some numerical examples are provided to illustrate the effect of input parameters on the probability characteristics of the system. IntroductionRecently, there has been an increasing interest in studying queueing systems when all the parameters are varying in time; see, for instance, [1]. This is due to the fact that these types of systems are more realistic and the periodic behavior of our daily live in different fields can be treated as well. Some of the examples are call centers, healthcare facilities, arrival and departure clearance for aircraft at airports, security checkpoints, automatic teller machines, multi-car dispatch of police and many others; see for instance [2][3][4] and references therein.Additionally, queueing models with impatient customers are the subject of research for many papers since they have many applications in telecommunication networks, inventory systems, and impatient

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“…Thus, usually the alternative way is taken: one resorts to different types of approximations. One can find an overview of the approaches for the performance evaluation of time-dependent queueing systems up to 2016 in [1]. The papers [2][3][4] are devoted to the construction of the main performance characteristics and papers [5][6][7][8] deal with the estimation of the convergence rate and approximations.…”

Section: Introductionmentioning

confidence: 99%

On the Rate of Convergence and Limiting Characteristics for a Nonstationary Queueing Model

2019

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Performance analysis of time-dependent queueing systems: Survey and classification

Cited by 80 publications

References 214 publications

New Analytic Solutions of Queueing System for Shared–Short Lanes at Unsignalized Intersections

New Analytic Solutions of Queueing System for Shared–Short Lanes at Unsignalized Intersections

On Probability Characteristics for a Class of Queueing Models with Impatient Customers

On the Rate of Convergence and Limiting Characteristics for a Nonstationary Queueing Model

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