Estimating disperse network queues

Gawlick, Rainer

doi:10.1145/381906.381944

Cited by 9 publications

(3 citation statements)

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“…In addition they address time-varying Poisson arrivals and arrivals with general interarrival time distributions. Gawlick (1990) applied this algorithm to transmission data from an ethernet line, stressing that non-Poisson arrival processes are then of real concern: for the case of an Erlang interarrival time distribution, our approach in Section 4 below gives a substantially faster algorithm by circumventing the numerical integration previously thought necessary.…”

Section: Introductionmentioning

confidence: 99%

Exploiting Markov chains to infer queue length from transactional data

Daley

Servi

1992

Journal of Applied Probability

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The use of taboo probabilities in Markov chains simplifies the task of calculating the queue-length distribution from data recording customer departure times and service commencement times such as might be available from automatic bank-teller machine transaction records or the output of telecommunication network nodes. For the case of Poisson arrivals, this permits the construction of a new simple exact O(n3) algorithm for busy periods with n customers and an O(n2 log n) algorithm which is empirically verified to be within any prespecified accuracy of the exact algorithm. The algorithm is extended to the case of Erlang-k interarrival times, and can also cope with finite buffers and the real-time estimates problem when the arrival rate is known.

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Section: Introductionmentioning

confidence: 99%

Exploiting Markov chains to infer queue length from transactional data

Daley

Servi

1992

Journal of Applied Probability

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“…Indeed, by implementing the Bertsimas and Servi algorithm, Gawlick [11] found the non-exponential version method to be prohibitively expensive:…”

Section: The Queue Inferencing Problemmentioning

confidence: 99%

Efficient computation of queueing delay at a network port from output link packet traces

Habib

Molle

2010

2010 22nd International Teletraffic Congress (lTC 22)

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Abstract-Current Internet core routers provide enough buffer capacity at each output port to keep the link busy for 250 msec. to avoid disrupting TCP flows because of dropped packets. Since link speeds are rising much more quickly than the availability and cost-effectiveness of large high-speed memories, there is now significant interest in reducing these buffers. Queue inferencing (QI) -a passive, external method for calculating the timedependent queue lengths and waiting times using start/end service event timestamps -is an ideal tool for studying the effects of such buffer size reductions because it can be applied in situ to packet traces collected from existing equipment carrying live traffic without any service disruptions. Although existing QI algorithms are too computationally expensive for this purpose, we observe that packet-sizes in a typical network trace are skewed towards a few "favored" sizes, and introduce two different methods for exploiting this property. First, since the output of a QI algorithm is a deterministic function of the service time sequence in a busy period, and our traces contain many repetitions of common packet-size sequences, we cache the output of the QI algorithm for later reuse. Second, we develop a new incremental QI algorithm, which can start from cached results for any prefix of the current busy period. Combining both methods leads us to structure the cache as a decision tree. Using network traces from WIDE project backbone to evaluate our method, we found that both the frequency of occurrence for particular busy periods and for busy-period lengths follow a decreasing power law, where busy periods lengths greater than 20 were very rare and none were greater than 70. Moreover, although we found that the size of the complete decision tree grows linearly with the length of the trace, we can restrict the tree to a finite number of "active" nodes (i.e., those nodes for which the probability of a visit is above some threshold) and use simple constant-time bounds to handle the rare exceptional cases.

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“…In the matrix, a "Y" ("N") implies that the test yields "yes" ("no") and thus the corresponding entry is 0 (positive). Note that all entries in the "southwest" implying that the desired probability is W3, 6 = 16/27.…”

Section: The Primary Recursive Algorithmsmentioning

confidence: 99%