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Heavytraffic limit theorems for the heavytailed GI/G/1 queue
, 1997
"... The classic GI=G=1 queueing model of which the tail of the service time and/or the interarrival time distribution behaves as t \Gammav S(t) for t !1, 1 ! v ! 2 and S(t) a slowly varying function at infinity, is investigated for the case that the traffic load a approaches one. Heavytraffic limit t ..."
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Cited by 1 (1 self)
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The classic GI=G=1 queueing model of which the tail of the service time and/or the interarrival time distribution behaves as t \Gammav S(t) for t !1, 1 ! v ! 2 and S(t) a slowly varying function at infinity, is investigated for the case that the traffic load a approaches one. Heavytraffic limit
Heavy Traffic Limit Theorems for Two Tandem Polling Stations
"... We consider two tandem singleserver stations in heavy traffic. There are two job types and they visit both stations in order. The first station processes jobs in an exhaustive service or gated service fashion and the second station uses an arbitrary nonidling service discipline. The stations have z ..."
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zero switchover times. We prove heavy traffic limit theorems for the twodimensional total workload processes, one under exhaustive service and one under gated service. The limiting processes are twodimensional reflected Brownian motions (RBM) and the limit under exhaustive service is equal
SOME EXTENSION OF THE HEAVY TRAFFIC LIMIT Theorem For The M/G/1—EPS Queue
, 2004
"... We extend the heavy traffic limit theorem for the stationary sojourn time distribution, suitably scaled, in the M/G/1 egalitarian processor sharing (EPS) queue from [12], [13] to the case when the M/G/1—EPS queue is modified by having K ≥ 0 extra permanent jobs with infinite sizes. ..."
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We extend the heavy traffic limit theorem for the stationary sojourn time distribution, suitably scaled, in the M/G/1 egalitarian processor sharing (EPS) queue from [12], [13] to the case when the M/G/1—EPS queue is modified by having K ≥ 0 extra permanent jobs with infinite sizes.
A Heavy Traffic Limit Theorem For Workload Processes With Heavy Tailed Service Requirements
 Management Science
, 1998
"... . A system with heavy tailed service requirements under heavy load having a single server, has an equilibrium waiting time distribution which is approximated by the MittagLeffler distribution. This fact is understood by a direct analysis of the weak convergence of a sequence of negative drift rand ..."
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Cited by 8 (2 self)
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random walks with heavy right tail and the associated all time maxima of these random walks. This approach complements the recent transform view of Boxma and Cohen [4]. 1. Introduction. Heavy traffic limit theorems were devised to study the behavior of complex networks. For economic reasons
Heavy Traffic Limit Theorems For The Closed LuKumar Network
, 2000
"... This paper contains more general results than are used here and applies to all twoserver balanced networks with certain types of nonidling service disciplines. It proves that the policy proposed by Harrison and Wein [14] is asymptotically optimal. Let U ..."
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This paper contains more general results than are used here and applies to all twoserver balanced networks with certain types of nonidling service disciplines. It proves that the policy proposed by Harrison and Wein [14] is asymptotically optimal. Let U
A Note on a Heavy Traffic Limit Theorem for the M/D/1—FBPS Queue
, 2004
"... In this short article we give a simple proof of the heavy traffic limit theorem for the sojourn time distribution, suitably scaled, in the M/D/1 queueing system under the foreground–background processor sharing (FBPS) discipline. The FBPS discipline gives the preemptive–resume priority in service t ..."
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In this short article we give a simple proof of the heavy traffic limit theorem for the sojourn time distribution, suitably scaled, in the M/D/1 queueing system under the foreground–background processor sharing (FBPS) discipline. The FBPS discipline gives the preemptive–resume priority in service
A Heavy Traffic Limit Theorem for a Class of Open Queueing Networks with Finite Buffers
, 1997
"... We consider a queueing network of d single server stations. Each station has a finite capacity waiting buffer, and all customers served at a station are homogeneous in terms of service requirements and routing. The routing is assumed to be deterministic and hence feedforward. A server stops working ..."
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Cited by 18 (4 self)
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to be used as an important ingredient in establishing heavy traffic limit theorems for general finite buffer networks. Key words and phrases: Finite capacity network, blocking probabilities, loss network, semimartingale reflecting Brownian motion, RBM, heavy traffic, limit theorems, oscillation estimates.
networks with finite buffers
, 1998
"... heavy traffic limit theorem for a class of open queueing ..."
and
, 2008
"... We establish a heavytraffic limit theorem on convergence in distribution for the number of customers in a manyserver queue. 1 ..."
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We establish a heavytraffic limit theorem on convergence in distribution for the number of customers in a manyserver queue. 1
Polling Systems with Periodic Server Routing in HeavyTraffic: Renewal Arrivals
"... This paper considers heavytraffic limit theorems for polling models with periodic server routing with general renewal arrivals and with mixtures of gated and exhaustive service policies, in a general parameter setting. We provide a strong conjecture for the limiting waitingtime distribution in a g ..."
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This paper considers heavytraffic limit theorems for polling models with periodic server routing with general renewal arrivals and with mixtures of gated and exhaustive service policies, in a general parameter setting. We provide a strong conjecture for the limiting waitingtime distribution in a
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