Queuing Problems with Heterogeneous Arrivals and Service

Yechiali, Uri; Naor, P.

doi:10.1287/opre.19.3.722

Cited by 162 publications

(103 citation statements)

References 6 publications

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“…Soon thereafter other researchers applied transforms and generating functions to related models: Neuts [20], Ç inlar [7,8], Arjas [3]. Yechiali and Naor [34] used generating functions to reduce the solution of our model to that of obtaining the roots of a cubic equation. Using similar techniques, de Smit [10] obtained a Weiner-Hopf factorization for systems with MAP arrivals and general service; Sengupta [29] analyzed a system with Markovian arrival and service distributions and service interruptions; Takine and Sengupta [32] generalized [29] to MAP arrivals and general service; Adan and Kulkarni [2] allowed dependencies between successive arrivals and services in a MAP/G/1 framework; and finally Harrison and Zatschler [12] numerically derived the entire sojourn time distribution for very general Markovian systems which they call G-Queues.…”

Section: Prior Workmentioning

confidence: 99%

Fundamental characteristics of queues with fluctuating load

Gupta

Wolf

Yechiali

2006

SIGMETRICS Perform. Eval. Rev.

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Systems whose arrival or service rates fluctuate over time are very common, but are still not well understood analytically. Stationary formulas are poor predictors of systems with fluctuating load. When the arrival and service processes fluctuate in a Markovian manner, computational methods, such as Matrix-analytic and spectral analysis have been instrumental in the numerical evaluation of quantities like mean response time. However, such computational tools provide only limited insight into the functional behavior of the system with respect to its primitive input parameters: the arrival rates, service rates, and rate of fluctuation.For example, the shape of the function that maps rate of fluctuation to mean response time is not well understood, even for an M/M/1 system. Is this function increasing, decreasing, monotonic? How is its shape affected by the primitive input parameters? Is there a simple closed-form approximation for the shape of this curve? Turning to user experience: How is the performance experienced by a user arriving into a "high load" period different from that of a user arriving into a "low load" period, or simply a random user. Are there stochastic relations between these? In this paper, we provide the first answers to these very fundamental questions.

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Section: Prior Workmentioning

confidence: 99%

Fundamental characteristics of queues with fluctuating load

Gupta

Wolf

Yechiali

2006

SIGMETRICS Perform. Eval. Rev.

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“…We use generating function technique [11] to solve the above system equations. Define the partial generating functions of the system as…”

Section: Performance Analysismentioning

confidence: 99%

Performance Analysis of a Delay-Tolerable Cognitive Radio Network

Tang¹,

Tang²

2017

Proceedings of the 2017 International Conference on Electronic Industry and Automation (EIA 2017)

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Abstract-In this paper, we analyze the performance of a delay-tolerable cognitive radio network at the call level, where secondary users detect and opportunistically access the channel resources when no primary users present. An ongoing secondary user using a channel may switch to another channel with some routing probability (due to the presence of a primary call) or leaves the channel (due to service completion) with some other probability. If the target channel is being used at that time, the secondary call will be placed in the queue of the channel. The queued secondary calls will reconnect back to the system when the channel becomes available. We develop a queueing network model for the system and solve the equilibrium system states by the generating function technique. Numerical results are presented to show the impact of system parameters on the performance metrics.

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“…We then use a MMPP, which has been parameterised using the autocorrelation function, to model correlated ATM traffic. The MMPP is a doubly stochastic Poisson process and was first used in queueing theory by Naor and Yelachi (17] and Neuts (18]. Poisson arrivals are generated by a source with rate governed by an m-state irreducible continuoustime Markov Chain (CTMC) which is independent of the instantaneous arrival process.…”

Section: The Mmpp Modelmentioning

confidence: 99%

Analysis and modelling of ATM (AAL5) traffic traces

Bhabuta

Harrison

2000

IFIP Advances in Information and Communication Technology

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We present an analysis of Asynchronous Transfer Mode {ATM) traffic data collected from the London MAN {Metropolitan Area Network). The traffic is found to have different characteristics depending on its intensity. The correlations between inter-arrival times of sessions for traffic from heavily utilised sites is insignificant at the 5% significance level and a Poisson Point process is thus appropriate as a model. Traffic from low utilisation sites, on the other hand, shows long-memory characteristics with correlation at lag 40 and more. This traffic is modelled firstly using an autoregressive process and then the well known Markov Modulated Poisson Process {MMPP). The burst size distribution for both correlated and uncorrelated traffic shows distinct peaks which corresponds to the fragmentation as data travels through networks with different Maximum Transport Units {MTUs).

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Queuing Problems with Heterogeneous Arrivals and Service

Cited by 162 publications

References 6 publications

Fundamental characteristics of queues with fluctuating load

Fundamental characteristics of queues with fluctuating load

Performance Analysis of a Delay-Tolerable Cognitive Radio Network

Analysis and modelling of ATM (AAL5) traffic traces

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