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HeavyTraffic Limits for Nearly Deterministic Queues
"... We establish heavytraffic limits for “nearly deterministic” queues, such as the G/D/n manyserver queue. Waiting times before starting service in the G/D/n queue are equivalent to waiting times in an associated Gn/D/1 model, where the Gn denotes “cyclic thinning ” of order n, indicating that the or ..."
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Cited by 4 (2 self)
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as n → ∞, where ρn is the traffic intensity in model n, and 0 < β < ∞. The nearly deterministic feature leads to interesting nonstandard scaling. We also establish revealing heavytraffic limits for the stationary waiting times and other performance measures in the Gn/Gn/1 queues, by letting ρn
THE HEAVYTRAFFIC BOTTLENECK PHENOMENON IN OPEN QUEUEING NETWORKS
, 1990
"... This note describes a simulation experiment involving nine exponential queues in series with a nonPoisson arrival process, which demonstrates that the heavytraffic bottleneck phenomenon can occur in practice (at reasonable traffic intensities) as well as in theory (in the limit). The results revea ..."
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Cited by 14 (6 self)
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This note describes a simulation experiment involving nine exponential queues in series with a nonPoisson arrival process, which demonstrates that the heavytraffic bottleneck phenomenon can occur in practice (at reasonable traffic intensities) as well as in theory (in the limit). The results
HeavyTraffic Revenue Maximization in Parallel Multiclass Queues
"... Motivated by revenue maximization in server farms with admission control, we investigate optimal scheduling in parallel processorsharing queues. Incoming customers are distinguished in multiple classes and we define revenue as a weighted sum of class throughputs. Under these assumptions, we describ ..."
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Cited by 1 (1 self)
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describe a heavytraffic limit for the revenue maximization problem and study the asymptotic properties of the optimization model as the number of clients increases. Our main result is a simple heuristic that is able to provide tight guarantees on the optimality gap of its solutions. In the general case
Applied Probability Trust (12 May 2011) HEAVYTRAFFIC LIMITS FOR NEARLY DETERMINISTIC QUEUES
"... We establish heavytraffic limits for nearly deterministic queues, such as the G/D/n manyserver queue. Since waiting times before starting service in the G/D/n queue are equivalent to waiting times in an associated Gn/D/1 model, where the Gn interarrival times are the sum of n consecutive interarri ..."
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We establish heavytraffic limits for nearly deterministic queues, such as the G/D/n manyserver queue. Since waiting times before starting service in the G/D/n queue are equivalent to waiting times in an associated Gn/D/1 model, where the Gn interarrival times are the sum of n consecutive
Efficiencydriven heavytraffic approximations for manyserver queues with abandonments
 Management Science
, 2004
"... Motivated by the desire to understand the performance of serviceoriented call centers, which often provide lowtomoderate quality of service, this paper investigates the efficiencydriven (ED) limiting regime for manyserver queues with abandonments. The starting point is the realization that, in ..."
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Cited by 79 (38 self)
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of delay necessarily approaches 1 in the ED regime, the ED regime can be realistic because, due to the abandonments, the delays need not be excessively large. This paper establishes ED manyserver heavytraffic limits and develops associated approximations for performance measures in the M/M/s/r + M model
© Institute of Mathematical Statistics, 2014 MANYSERVER HEAVYTRAFFIC LIMIT FOR QUEUES WITH
"... A manyserver heavytraffic FCLT is proved for the Gt/M/st + GI queueing model, having timevarying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment according to a general probability distribution. The FCLT provides theoreti ..."
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A manyserver heavytraffic FCLT is proved for the Gt/M/st + GI queueing model, having timevarying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment according to a general probability distribution. The FCLT provides
DISTRIBUTED SYSTEMS
, 1985
"... Growth of distributed systems has attained unstoppable momentum. If we better understood how to think about, analyze, and design distributed systems, we could direct their implementation with more confidence. ..."
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Cited by 755 (1 self)
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Growth of distributed systems has attained unstoppable momentum. If we better understood how to think about, analyze, and design distributed systems, we could direct their implementation with more confidence.
Analysis, Modeling and Generation of SelfSimilar VBR Video Traffic
, 1994
"... We present a detailed statistical analysis of a 2hour long empirical sample of VBR video. The sample was obtained by applying a simple intraframe video compression code to an action movie. The main findings of our analysis are (1) the tail behavior of the marginal bandwidth distribution can be accu ..."
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Cited by 546 (6 self)
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be accurately described using "heavytailed" distributions (e.g., Pareto); (2) the autocorrelation of the VBR video sequence decays hyperbolically (equivalent to longrange dependence) and can be modeled using selfsimilar processes. We combine our findings in a new (nonMarkovian) source model
Results 1  10
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