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97
Sampling At Subexponential Times, With Queueing Applications
, 1998
"... We study the tail asymptotics of the r.v. X(T ) where fX(t)g is a stochastic process with a linear drift and satisfying some regularity conditions like a central limit theorem and a large deviations principle, and T is an independent r.v. with a subexponential distribution. We find that the tail of ..."
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Cited by 59 (4 self)
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We study the tail asymptotics of the r.v. X(T ) where fX(t)g is a stochastic process with a linear drift and satisfying some regularity conditions like a central limit theorem and a large deviations principle, and T is an independent r.v. with a subexponential distribution. We find that the tail of X(T ) is sensitive to whether or not T has a heavier or lighter tail than a Weibull distribution with tail e \Gamma p x . This leads to two distinct cases, heavy-tailed and moderately heavy-tailed, but also some results for the classical light-tailed case are given. The results are applied via distributional Little's law to establish tail asymptotics for steady--state queue length in GI/GI/1 queues with subexponential service times. Further applications are given for queues with vacations, and M/G/1 busy periods.
Useful martingales for stochastic storage processes with Lévy input
- J. Appl. Probab
, 1992
"... In this paper we generalize the martingale of Kella and Whitt to the setting of Lévy-type processes and show that under some quite minimal conditions the local martingales are actually L 2 martingales which upon dividing by the time index converge to zero a.s. and in L 2. We apply these results to g ..."
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Cited by 48 (14 self)
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In this paper we generalize the martingale of Kella and Whitt to the setting of Lévy-type processes and show that under some quite minimal conditions the local martingales are actually L 2 martingales which upon dividing by the time index converge to zero a.s. and in L 2. We apply these results to generalize known decomposition results for Lévy queues with secondary jump inputs and queues with server vacations or service interruptions. Special cases are polling systems with either compound Poisson or more general Lévy inputs. Keywords: Lévy-type processes, Lévy storage systems, Kella-Whitt martingale, decomposition results, queues with server vacations
On a Two-Queue Priority System with Impatience and its Application to a Call Center
, 1998
"... We consider a s-server system with two FCFS queues, where the arrival rates at the queues and the service rate may depend on the number n of customers being in service or in the first queue, but the service rate is assumed to be constant for n ? s. The customers in the first queue are impatient. If ..."
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Cited by 28 (1 self)
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We consider a s-server system with two FCFS queues, where the arrival rates at the queues and the service rate may depend on the number n of customers being in service or in the first queue, but the service rate is assumed to be constant for n ? s. The customers in the first queue are impatient. If the offered waiting time exceeds a random maximal waiting time I , then the customer leaves the first queue after time I . If I is less than a given deterministic time then he leaves the system else he transits to the end of the second queue. The customers in the first queue have priority. The service of a customer from the second queue will be started if the first queue is empty and more than a given number of servers become idle. For the model being a generalization of the M(n)=M(n)=s+GI system balance conditions for the density of the stationary state process are derived yielding the stability conditions and the probabilities that precisely n customers are in service or in the first queue...
Performance Analysis of the CRMA-Protocol in High-Speed Networks
, 1990
"... In this paper a performance analysis of the CRMA medium access protocol is presented. The CRMA (Cyclic Reservation Multiple Access) scheme is proposed as an access mechanism for high-speed LANs and MANs. An approximate computational method is derived to obtain the distribution functions of performan ..."
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Cited by 24 (0 self)
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In this paper a performance analysis of the CRMA medium access protocol is presented. The CRMA (Cyclic Reservation Multiple Access) scheme is proposed as an access mechanism for high-speed LANs and MANs. An approximate computational method is derived to obtain the distribution functions of performance measures of interest like the medium access delay and the packet transfer time. The analysis is done using a decomposition approach for the access delay in conjunction with a G/G/1 queue with feedback and a M/G/1 queue with server vacation, observed in discrete-time domain. The reservation-cancelation backpressure mechanism is also taken into account in the model. Numerical results are obtained to investigate the efficiency of the backpressure scheme and the scaling issues of the interreserve interval under various load conditions and system configurations. Furthermore, results addressing performance aspects like the fairness issues, the jitter of maximum access delay and the system behavior under stationwise saturated conditions are also discussed. 1 The CRMA-Protocol The Cylic-Reservation Multiple-Access (CRMA) protocol has been proposed recently as access scheme for high-speed LANs and MANs, especially in the network capacity region beyond 1 Gbit/sec. The proposed protocol can be used in unidirectional folded-bus or dual-bus topologies. Detail descriptions of the CRMA access scheme with various bus structures can be found in [9] and [10]. From performance analysis point ofview, there is a few studies dealing with modelling aspects of the CRMA protocol. In [2] analytic results for the mean values of the access delay arediscussed, comparing different reservation mechanisms. A simulation study of the CRMA protocol is given in [7]. Simulation results are also obtained in [8...
Polling models with and without switchover times
- Oper. Res
, 1997
"... Consider a single-server cyclic polling system: a single server S visits n queues Q1; : : : ; Qn in cyclic order, serving customers at Qi according to some service disci1 ..."
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Cited by 23 (6 self)
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Consider a single-server cyclic polling system: a single server S visits n queues Q1; : : : ; Qn in cyclic order, serving customers at Qi according to some service disci1
Optimization Of Multiclass Queueing Networks with Changeover Times via the Achievable Region Approach: Part I, The Single-station Case
, 1999
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Analysis of multi-server systems via dimensionality reduction of Markov chains
- School of Computer Science, Carnegie Mellon University
, 2005
"... The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chai ..."
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Cited by 20 (4 self)
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The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chains (DR). Moment matching algorithms allow us to approximate a general distribution with a phase type (PH) distribution. Our moment matching algorithms improve upon existing ones with respect to the computational efficiency (we provide closed form solutions) as well as the quality and generality of the solution (the first three moments of almost any nonnegative distribution are matched). Approximating job size and interarrival time distributions by PH distributions enables modeling a multiserver system by a Markov chain, so that the performance of the system is given by analyzing the Markov chain. However, when the multiserver system involves resource sharing or prioritization, the Markov chain often has a multidimensionally infinite state space, which makes the analysis computationally hard. DR allows us to closely approximate a multidimensionally infinite Markov chain with a Markov
Multi-product systems with both setup times and costs: Fluid bounds and schedules
- Operations Research
, 2004
"... This paper considers a multi-product, single-server production system where both setup times and costs are incurred whenever the server changes product. The system is make-to-order with a per unit backlogging cost. The objective is to minimize the long-run average cost per unit time. Using a fluid m ..."
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Cited by 18 (0 self)
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This paper considers a multi-product, single-server production system where both setup times and costs are incurred whenever the server changes product. The system is make-to-order with a per unit backlogging cost. The objective is to minimize the long-run average cost per unit time. Using a fluid model, we provide a closed-form lower bound on system performance. This bound is also shown to provide a lower bound for stochastic systems when scheduling is static, but is only an approximation when scheduling is dynamic. Heavy-traffic analysis yields a refined bound that includes second-moment terms. The fluid bound suggests both dynamic and static scheduling In this paper we consider a production environment where a number of different products are produced on a single machine and setup activities are necessary when switches of product type are made. These setup activities require both time and cost that depend on the specific product type. Throughout the paper we assume that the setups do not depend on the previous product produced
Analysis of an M/G/1 queue with repeated inhomogeneous vacations Application to IEEE 802.16e power saving
, 2008
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Analysis of cycle stealing with switching times and thresholds
- Perf. Eval
, 2005
"... We consider two processors, each serving its own M/GI/1 queue, where one of the processors (the “donor”) can help the other processor (the “beneficiary”) with its jobs, during times when the donor processor is idle. That is the beneficiary processor “steals idle cycles ” from the donor processor. Th ..."
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Cited by 15 (4 self)
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We consider two processors, each serving its own M/GI/1 queue, where one of the processors (the “donor”) can help the other processor (the “beneficiary”) with its jobs, during times when the donor processor is idle. That is the beneficiary processor “steals idle cycles ” from the donor processor. There is a switching time required for the donor processor to start working on the beneficiary jobs, as well as a switching back time. We also allow for threshold constraints on both the beneficiary and donor sides, whereby the decision to help is based not only on idleness but also on satisfying threshold criteria in the number of jobs. We analyze the mean response time for the donor and beneficiary processors. Our analysis is approximate, but can be made as accurate as desired, and is validated via simulation. Results of the analysis illuminate principles on the general benefits of cycle stealing and the design of cycle stealing policies.
