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( hN, and given that we now find independence of classes at each departure, then the departure process for multiple substrates strongly resembles independent Poisson processes for each class, as is found ... For example, in quasi-reversible multiclass queueing networks [38, 43, 47, 48] , the departure process is equivalent to the superposition of independent Poisson processes for each substrate class. ... The more general case of queueing systems with unoccupied sites can be done by also constraining known probabilities Pr(M ¼ Q(q)) for occupancy (equation (B 1)). We do not perform these steps here. ...doi:10.1098/rsfs.2013.0077 pmid:24904740 pmcid:PMC3996589 fatcat:wfo5a3utznftnez6r6h66ocgq4
Summary: “This paper discusses an approximation for single-class departure processes from multi-class queues: If the arrival rate of one class upon one visit to the queue is a small proportion of the to ... Numerical studies on IPA convergence properties are also presented.” 89i:90037 90B22 Whitt, Ward (1-BELL) A light-traffic approximation for single-class departure processes from multi-class queues. ...
Methods are developed for approximately characterizing the departure process of each customer class from a multi-class single-server queue with unlimited waiting space and the firstin first-out service ... With all procedures proposed here, the approximate variability parameter of the departure process of each class is a linear function of the variability parameters of the arrival processes of all the classes ... Approximate single-class departure-process variability parameters c d1 2 for one multi-class queue with independent and identically distributed component streams and service times: the case of ρ = 0. 9 ...doi:10.1007/bf02024659 fatcat:gxfonvmhffbatlwdeudheq2tqu
Based on further experiments, it is conjectured that departure processes with relative dynamic priority are indeed Poisson in two class exponential queue. ... Many device to device communication networks can be modelled by multi-class tandem queues. In many applications, it is desired to have different quality of service for various classes. ... Results on departure process of multi class queues with strict priority are explored in literature (see  ). ...doi:10.1109/wiopt.2015.7151062 dblp:conf/wiopt/MayekarVGH15 fatcat:4g2kv7yzwnbizhiw46l43d5zpi
In this paper, the problem of determining optimal booking policy for multiple fare classes in a pool of identical seats for multi‐leg flights is considered. ... This paper presents static and dynamic models of airline seat inventory control for multi‐leg flights with multiple fare classes, which allow one to maximize the expected contribution to profit. ... We present an optimal dynamic reservation policy that is used at each stage prior to departure time for multi-leg flights with several classes of passenger service. ...doi:10.3846/16487788.2004.9635883 fatcat:tqdyobhmxzdxxd5b5viyru2lty
We apply the multi-class extension of MAP, referred to as Marked MAP (MMAP), for the description of the input and internal traffic in the queueing network. ... Marked Markov arrival process MMAP/MAP/1 queue Priority service Moments based analysis Output process a b s t r a c t This paper presents a Markov arrival process (MAP) based methodology for the analysis ... We will use this result for constructing an MMAP to approximate the departure process of a queueing network node. ...doi:10.1016/j.comnet.2009.02.016 fatcat:iq7zat2j5nh7fnnqhvpwzeevze
Stochastic processing networks arise as models in manufacturing, telecommunications, transportation, computer systems, the customer service industry and biochemical reaction networks. ... Common characteristics of these networks are that they have entities, such as jobs, packets, vehicles, customers or molecules, that move along routes, wait in buffers, receive processing from various resources ... Some Approximations for Multi-Class Queues and Networks For multi-class queues, early on, Whitt (1971) proved a heavy traffic limit theorem for a multi-class queue with static priority service. ...doi:10.1146/annurev-statistics-010814-020141 fatcat:7mcq3ujtrnh4jnx63kp7xpgydy
The purpose of the paper is to construct asymptotic expansions for the partition function G for multi-class networks under three assumptions: (i) the number of single-server, fixed-rate nodes is large; ... , GA) Little laws for utility processes and waiting times in queues. ...
In this paper we propose a family of finite approximations for the departure process of an ME/ME/1 queue indexed by a parameter k defined as the system size of the finite approximation. ... The approximations capture the interdeparture times from an ME/ME/1 queue exactly and preserve the lag correlations of inter-event times of the departures from an ME/ME/1 queue up to lag (k − 1). ... Current work also involves using our approximation in studying the departure process of a tagged stream from a multi-class queue. ...doi:10.1051/ro:2004018 fatcat:lyecma3xfndqlcrtemzq5j2yki
; Ulm) Light-traffic approximations for Markov-modulated multi-server queues. ... The idea of factorial moment expansion is applied in order to derive approximation formulas for stationary characteris- tics of multi-server queues with Markov-modulated arrival process and with the first-come-first-served ...
One of the most fundamental properties that single-server multi-class service systems may possess is the property of work conservation. ... This paper is devoted to single-server multi-class service systems in which work conservation is violated in the sense that the server's activities may be interrupted although work is still present. ... Wang and several other colleagues for interesting discussions and for useful comments on an earlier draft of this paper. ...doi:10.1007/bf01149192 fatcat:5yxc5drj6vaypfubuthbctwfve
presents an adaptive queue management scheme to maintain queuing delay in a router at a required level based on a comprehensive analytical model under aggregated Internet traffic flows from various traffic classes ... is developed to derive the relationship between average queuing delays and queuing thresholds based on a traffic model that models aggregated Internet traffic through superposition of N MMBP-2 arrival processes ... Nevertheless, a single MMBP-2 arrival process is not able to represent multi-class aggregated Internet traffic. ...doi:10.1016/j.jcss.2010.08.007 fatcat:7owc4drbsbdrrmzoqs7mtz6o3y
To our knowledge, this is the first analysis of a multi-input multi-output queueing network yielding exact solutions for general arrival processes. ... Arrivals and departures take place at each stage according to arbitrary stochastic processes. ... Equivalently representing the departure process of the final node in a multi-input single output tandem with delayed versions of the original inputs, where the time delay for the k th input stream is given ...doi:10.1109/icc.2004.1312912 dblp:conf/icc/Neely04 fatcat:li5b2x5gdzapjpywyc6o7cc3xi
A large deviation principle for the stationary distribution of these multi-class queueing networks is also found. Its rate function has a dual form that coincides with proportional fairness. ... We consider multi-class single-server queueing networks that have a product form stationary distribution. ... I would like to thank Alexandre Proutière for various comments that have improved the content and context of this paper. ...doi:10.1214/09-aap612 fatcat:fwvtvqqf75fivokrclsctkdyly
In this system, it uses the Class Constraint Bin Packing (CCBP) algorithm and semi online color set algorithm which saves the energy by reducing server and gives the good satisfaction ratio. ... RELATED WORK On Multi-dimensional Packing Problems; system studies the approximateness of multi-dimensional generalizations of three classical packing problems: multiprocessor scheduling, bin packing, ... Instead they focus on proving the bounds on the approximation ratio for any removal algorithm. In result it does not apply here because they do not repack items after the departure. ...doi:10.5120/ijca2016910840 fatcat:sbky6utt2vc4howm5byyrhw3kq
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