Some consequences of estimating parameters for the M/M/1 queue

Schruben, Lee W.; Kulkarni, Radhika V.

doi:10.1016/0167-6377(82)90051-7

Cited by 36 publications

(13 citation statements)

References 2 publications

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“…Since the rates are constant, we can observe the system in steady state for a long time. This means that we can assume we have enough data on our own arrival and service process (λ v and µ v , or just ρ v ) and on the blocking probability that we do not need to consider uncertainty in our estimates; for discussions of estimating our own rates, see [13,21].…”

Section: The Homogeneous Casementioning

confidence: 99%

Estimating Effective Capacity in Erlang Loss Systems under Competition

Ross

Shanthikumar

2005

Queueing Syst

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We consider an Erlang loss system (modem bank) with two streams of arriving customers, where arrival rates vary by time-of-day. We can observe one of the traffic streams (our customers), but we do not know how many servers the system has, or the characteristics of the other stream. Using detailed samplepath data, we construct a maximum likelihood estimator that makes good use of the data, but is slow to evaluate. As an alternative, we present an estimation system based on traffic data summarized by hour. This estimation system is much faster, and tends to produce good lower bounds on the size of the system and competing traffic.

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Section: The Homogeneous Casementioning

confidence: 99%

Estimating Effective Capacity in Erlang Loss Systems under Competition

Ross

Shanthikumar

2005

Queueing Syst

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“…Equation (2) disqualifiesρ naive /(1 −ρ naive ) as a good estimate of the expected number of customers in the system (in the limit) of a stable M/M/1 queue. The fact that ratios of estimators in queueing processes may have undesirable sampling properties stems from Schruben and Kulkarni [7]. Zheng and Selia [8] construct alternative estimators for the limiting expected number of customers in queue (and several other performance measures) that have better sampling properties.…”

Section: Introductionmentioning

confidence: 99%

“…The most basic estimator of ρ is perhaps the naive ratio estimatorρ [7] and Zheng and Seila [8] for the M/M/1 queue, where it was noted that ρ naive frequently exceeds unity with positive probability and…”

Section: Introductionmentioning

confidence: 99%

Technical note: Traffic intensity estimation

Kiessler

Lund

2009

Naval Research Logistics

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“…Inferential methods from classical and Bayesian statistics have been previously described. In regard to classical statistical methods, Clark [9] presented a maximum likelihood estimator and approximations for λ and μ, and Schruben and Kulkarni [10] showed that estimating the arrival rates and mean service times (1 / μ) may result in a noticeable difference between the estimated model and the real system. More recently, Kannan and Jabarali [11] described an application of M/M/1 queues and presented maximum likelihood estimates for queues formed along two periods, namely normal demand periods and holidays.…”

Section: Introductionmentioning

confidence: 99%

Bayesian sample sizes in an M/M/1 queueing systems

Quinino

Cruz

2016

Int J Adv Manuf Technol

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Although the broad field of applications amply justifies an intensive study of queueing models, it turned out that these models are also of great use outside the field of queueing theory, e.g., in inventory and maintenance theory very important for production systems. In these applications, the queue model M/M/1 has several works that illustrate its importance, but usually, they adopt the parameters known. The literature presents estimation methods such as maximum likelihood and Bayesian that could be directly applied. However, there is no discussion about planning the sample size to guarantee the precision of the parameters that are estimated. An accurate estimate of the model parameters can avoid wrong decisions on inventory control and maintenance. The focus here is on sample size determination for estimates in single-server Markovian infinity queues, considered the simplest and yet most useful queueing model for its accuracy to model many problems of practical interest. In this article, a Bayesian method is described for sample size determination for traffic intensity estimation, one of the most important parameters for performance evaluation of queueing systems. Numerical results are presented to attest to the efficiency and efficacy of the approach.

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Some consequences of estimating parameters for the M/M/1 queue

Cited by 36 publications

References 2 publications

Estimating Effective Capacity in Erlang Loss Systems under Competition

Estimating Effective Capacity in Erlang Loss Systems under Competition

Technical note: Traffic intensity estimation

Bayesian sample sizes in an M/M/1 queueing systems

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