Modeling Traffic Flows With Queueing Models: A Review

Woensel, Tom Van; Vandaele, Nico

doi:10.1142/s0217595907001383

Cited by 103 publications

(54 citation statements)

References 42 publications

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“…In these systems jobs arrive, are served in parallel, to leave when their service is completed. While rooted in communication networks, where the so-called Erlang model describes the dynamics of the number of calls in progress, applications in various other domains have been explored, such as road traffic [19] and biology [16,17]. In the standard infinite-server model, referred to as M/G/∞, jobs arrive according to a Poisson process with rate λ, where their service times form a sequence of independent and identically distributed (i.i.d.)…”

Section: Introductionmentioning

confidence: 99%

Large deviations of an infinite-server system with a linearly scaled background process

Turck

Mandjes

2014

Performance Evaluation

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ABSTRACT. This paper studies an infinite-server queue in a Markov environment, that is, an infiniteserver queue with arrival rates and service times depending on the state of a Markovian background process. We focus on the probability that the number of jobs in the system attains an unusually high value. Scaling the arrival rates λ i by a factor N and the transition rates ν ij of the background process as well, a large-deviations based approach is used to examine such tail probabilities (where N tends to ∞). The paper also presents qualitative properties of the system's behavior conditional on the rare event under consideration happening.

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Section: Introductionmentioning

confidence: 99%

Large deviations of an infinite-server system with a linearly scaled background process

Turck

Mandjes

2014

Performance Evaluation

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“…Nodes represent road segments and nodes with infinite supply model road segments with an on-ramp, where it is assumed that there is constant flow of incoming traffic to the on-ramp. Note that in queueing models for traffic systems one typically only models the flow in one direction and fits the service rate of the queues to the traffic characteristics; see, for example [21,23].…”

Section: Example Of Breakdown and Repair Processmentioning

confidence: 99%

“…We have to show that the distribution given by (16) Under the required condition of either (8) and (9) solves balance equations (23). The last step of proving the theorem is by normalizingπ , which is possible because η i < μ i holds for all i ∈ W .…”

Section: B Proof Of Theoremmentioning

confidence: 99%

Analysis of Jackson networks with infinite supply and unreliable nodes

et al. 2017

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Jackson networks are versatile models for analyzing complex networks. In this paper we study generalized Jackson networks with single-server stations, where nodes may have an infinite supply of work. We allow simultaneous breakdown of servers and consider group repair strategies. We establish the existence of a steadystate distribution of the queue-length vector at stable nodes for different types of failure regimes. In steady state the distribution of the failure/repair regime and of the queuelength vector at stable nodes decouples in a product-form way. We provide closed-form solutions for the classical performance measures such as throughput or mean sojourn time at a station.

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“…In this setting, it is the sharing of the same storage capacity and the strict adherence to the first-come-first-served (FCFS) service discipline that causes interaction between the various customer classes. Some obvious practical applications of this kind of model occur in the context of road networks (see, e.g., [22,30,29,10]), when cars having different destinations use the same road section in front of a traffic junction, or input queues in the context of packet switches in the nodes of communication networks (see, e.g. [24,4]), when information packets destined to different downstream nodes are stored in shared buffers.…”

Section: Introduction and Mathematical Modelmentioning

confidence: 99%

Performance analysis of a discrete-time two-class global-FCFS queue with two servers and geometric service times

Bruneel

Mlange

Walraevens

et al. 2017

Performance Evaluation

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In this paper, we analyze a discrete-time queueing model with two types (classes) of customers and two servers, one for each customer class. Although each server can only process one type of customers, all customers are accommodated in one single queue and served in their order of arrival, irrespective of their types. The numbers of customers arriving in the system from time slot to time slot are independent, but the types of consecutive customers are not necessarily independent. Specifically, we assume that a first-order Markovian correlation ("interclass correlation") exists between the types of subsequent customers in the arrival stream. The fact that multiple customers of the same type may arrive back-to-back and customers have to be served in their order of arrival, causes occasional under-utilization of the service capacity of the system, because some customers may not be able to reach their server owing to the presence of customers of the opposite type in front of them.In this paper, we assume that the service times of both types of customers are independent, geometrically distributed random variables. The paper extends earlier work where all the service times were assumed to be of fixed length, either equal to 1 slot each, or equal to multiple slots. The fact that, in the present paper, service times are of variable length, entails that customers being served simultaneously can overtake each other, thus disturbing the original arrival order. This phenomenon did not occur in previous studies with fixed-length service times, and represents the main new element of the paper. It also complicates the analysis of the system considerably. Nevertheless, we are able to derive explicit expressions for the probability generating functions and the mean values of the main performance measures of the system, in terms of the original system parameters and one root of a non-linear equation. Our results reveal the impact of the interclass correlation and the variable nature of the service times on the achievable throughput, the (mean) number of customers in the system, the (mean) customer sojourn times, the (mean) unfinished work in the system, and related quantities.

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Modeling Traffic Flows With Queueing Models: A Review

Cited by 103 publications

References 42 publications

Large deviations of an infinite-server system with a linearly scaled background process

Large deviations of an infinite-server system with a linearly scaled background process

Analysis of Jackson networks with infinite supply and unreliable nodes

Performance analysis of a discrete-time two-class global-FCFS queue with two servers and geometric service times

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