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208
Stability and Convergence of Moments for Multiclass Queueing Networks via Fluid Limit Models
 IEEE Transactions on Automatic Control
, 1995
"... The subject of this paper is open multiclass queueing networks, which are common models of communication networks, and complex manufacturing systems such as wafer fabrication facilities. We provide sufficient conditions for the existence of bounds on longrun average moments of the queue lengths at ..."
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Cited by 113 (37 self)
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The subject of this paper is open multiclass queueing networks, which are common models of communication networks, and complex manufacturing systems such as wafer fabrication facilities. We provide sufficient conditions for the existence of bounds on longrun average moments of the queue lengths at the various stations, and we bound the rate of convergence of the mean queue length to its steady state value. Our work provides a solid foundation for performance analysis either by analytical methods or by simulation. These results are applied to several examples including reentrant lines, generalized Jackson networks, and a general polling model as found in computer networks applications. Keywords: Multiclass queueing networks, ergodicity, general state space Markov processes, polling models, generalized Jackson networks, stability, performance analysis. 1 Introduction The subject of this paper is open multiclass queueing networks, which are models of complex systems such as wafer fabri...
Optimal Robot Scheduling for Web Search Engines
, 1997
"... A robot is deployed by a Web search engine in order to maintain the currency of its data base of Web pages. This paper studies robot scheduling policies that minimize the fractions r i of time pages spend outofdate, assuming independent Poisson pagechange processes, and a general distribution fo ..."
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Cited by 76 (1 self)
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A robot is deployed by a Web search engine in order to maintain the currency of its data base of Web pages. This paper studies robot scheduling policies that minimize the fractions r i of time pages spend outofdate, assuming independent Poisson pagechange processes, and a general distribution for the page access time X . We show that, if X is decreased in the increasingconvex ordering sense, then r i is decreased for all i under any scheduling policy, and that, in order to minimize expected total obsolescence time of any page, the accesses to that page should be as evenly spaced in time as possible. We then investigate the problem of scheduling to minimize the cost function P c i r i ; where the c i are given weights proportional to the pagechange rates ¯ i . We give a tight bound on the performance of such a policy and prove that the optimal frequency at which the robot should access page i is proportional to ln(h i ) \Gamma1 , where h i := Ee \Gamma¯ i X : Note that this...
Stochastic and dynamic vehicle routing in the Euclidean Plane: The MultipleServer, Capacitated Vehicle Case
, 1990
"... In a previous paper [12], we introduced a new model for stochastic and dynamic vehicle routing called the dynamic traveling repairman problem (DTRP), in which a vehicle traveling at constant velocity in a Euclidean region must service demands whose time of arrival, location and onsite service are s ..."
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Cited by 67 (0 self)
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In a previous paper [12], we introduced a new model for stochastic and dynamic vehicle routing called the dynamic traveling repairman problem (DTRP), in which a vehicle traveling at constant velocity in a Euclidean region must service demands whose time of arrival, location and onsite service are stochastic. The objective is to find a policy to service demands over an infinite horizon that minimizes the expected system time (wait plus service) of the demands. We showed that the stability condition did not depend on the geometry of the service region (i.e. size, shape, etc.). In addition, we established bounds on the optimal system time and proposed an optimal policy in light traffic and several policies that have system times within a constant factor of the lower bounds in heavy traffic. We showed that the leading behavior of the optimal system time had a particularly simple form which increases much more rapidly with traffic intensity than the system time in traditional queues (e.g. M/G/1). In this paper, we extend these results in several directions. First, we propose new bounds and policies for the problem of m identical vehicles with unlimited capacity and show that in heavy traffic the system time is reduced by a factor of 1/m² over the single server case. Policies based on dividing the service region into m equal subregions
Polling Systems with Zero Switchover Times: A HeavyTraffic Averaging Principle
, 1993
"... In polling systems, M 2 queues are visited by a single server in cyclic order. These systems model such diverse applications as tokenring communication networks and cyclic production systems. We study polling systems with exhaustive service and zero switchover (walk) times. Under standard heavytr ..."
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Cited by 42 (4 self)
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In polling systems, M 2 queues are visited by a single server in cyclic order. These systems model such diverse applications as tokenring communication networks and cyclic production systems. We study polling systems with exhaustive service and zero switchover (walk) times. Under standard heavytraffic assumptions and scalings, the total unfinished work converges to a onedimensional reflected Brownian motion, whereas the workloads of individual queues change at a rate that becomes infinite in the limit. Although it is impossible to obtain a multidimensional limit process in the usual sense, we obtain an `averaging principle' for the individual workloads. To illustrate the use of this principle, we calculate a heavytraffic estimate of waiting times. Keywords: Polling systems, cyclic servers, diffusion approximations, heavytraffic limits. June 21, 1995 The research of this author was supported in part under contract with AT&T Bell Laboratories, and in part under a grant from the I...
Dynamic Scheduling of a TwoClass Queue with Setups
, 1994
"... We analyze two scheduling problems for a queueing system with a single server and two customer classes. Each class has its own renewal arrival process, general service time distribution, and holding cost rate. In the first problem, a setup cost is incurred when the server switches from one class to ..."
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Cited by 36 (3 self)
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We analyze two scheduling problems for a queueing system with a single server and two customer classes. Each class has its own renewal arrival process, general service time distribution, and holding cost rate. In the first problem, a setup cost is incurred when the server switches from one class to the other, and the objective is to minimize the longrun expected average cost of holding customers and incurring setups. The setup cost is replaced by a setup time in the second problem, where the objective is to minimize the average holding cost. By assuming that a recently derived heavy traffic principle holds not only for the exhaustive policy but for nonexhaustive policies, we approximate (under standard heavy traffic conditions) the dynamic scheduling problems by diffusion control problems. The diffusion control problem for the setup cost problem is solved exactly, and asymptotics are used to analyze the corresponding setup time problem. Computational results show that the proposed scheduling policies are within several percent of optimal over a broad range of problem parameters. We consider two dynamic scheduling problems for a singleserver queueing system with two classes of customers. In both problems, each class possesses its own renewal arrival process, general service time distribution, and holding cost rate, and the server incurs a setup when switching from one class to the other. In the setup cost
A Queueing Network With A Single Cyclically Roving Server
 Queueing Systems
, 1988
"... A queueing network that is served by a single server in a cyclic order is analyzed in this paper. Customers arrive at the queues from outside the network according to independent Poisson processes. Upon completion of his service, a customer may leave the network, be routed to another queue in the ne ..."
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Cited by 33 (1 self)
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A queueing network that is served by a single server in a cyclic order is analyzed in this paper. Customers arrive at the queues from outside the network according to independent Poisson processes. Upon completion of his service, a customer may leave the network, be routed to another queue in the network or rejoin the same queue for another portion of service. The single server through the different queues of the network in a cyclic manner. Whenever the server arrives at a queue (polls the queue), he serves the waiting customers in that queue according to some service discipline. Both the gated and the exhaustive disciplines are considered. When moving from one queue to the next queue, the server incurs a switchover period. This queueing network model has great many applications in communication, computer, robotics and manufacturing systems. Examples include token rings, singleprocessor multitask systems and others. For this model we derive the generating function and the expected ...
On the Impact of IEEE 802.11 MAC on Traffic Characteristics
 IEEE Journal on Selected Areas in Communications
, 2003
"... IEEE 802.11 MAC is gaining widespread popularity as a layer2 protocol for wireless local area networks. While efforts have been made recently to evaluate the performance of various protocols in wireless networks and to evaluate the capacity of wireless networks, very little is understood or known a ..."
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Cited by 27 (5 self)
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IEEE 802.11 MAC is gaining widespread popularity as a layer2 protocol for wireless local area networks. While efforts have been made recently to evaluate the performance of various protocols in wireless networks and to evaluate the capacity of wireless networks, very little is understood or known about the traffic characteristics of wireless networks. In this paper we address this issue and first develop an analytic model to characterize the interarrival time distribution of traffic in wireless networks with fixed base stations or ad hoc networks using the 802.11 MAC. Our analytic model and supporting simulation results show that the 802.11 MAC can induce pacing in the traffic and the resulting interarrival times are best characterized by a multimodal distribution. This is a sharp departure from behavior in wired network and can significantly alter the second order characteristics of the traffic, which forms the second part of our study. Through simulations we show that while the traffic patterns at the individual sources are more consistent with longrange dependence and selfsimilarity, in contrast to wired networks, the aggregate traffic is not selfsimilar. The aggregate traffic is better classified as a multifractal process and we conjecture that the various peaks of the multimodal interarrival time distribution have a direct contribution to the differing scaling exponents at various timescales.
Optimization Of Multiclass Queueing Networks with Changeover Times via the Achievable Region Approach: Part I, The Singlestation Case
, 1999
"... ..."
Capacity and delay analysis of nextgeneration passive optical networks (NGPONs)–extended version
 Rutgers Univ., Univ. of Rochester, Warwick Univ., and
, 2010
"... counts, and fiber lengths, as well as ( ..."
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