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Combinatorial Optimization Problems For Which Almost Every Algorithm Is Asymptotically Optimal!
 Optimization
, 1994
"... Consider a class of optimization problems for which the cardinality of the set of feasible solutions is m and the size of every feasible solution is N . We prove in a general probabilistic framework that the value of the optimal solution and the value of the worst solution are asymptotically almost ..."
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Cited by 12 (1 self)
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Consider a class of optimization problems for which the cardinality of the set of feasible solutions is m and the size of every feasible solution is N . We prove in a general probabilistic framework that the value of the optimal solution and the value of the worst solution are asymptotically almost surely (a.s.) the same provided log m = o(N) as N and m become large. This result implies that for such a class of combinatorial optimization problems almost every algorithm finds asymptotically optimal solution! The quadratic assignment problem, the location problem on graphs, and a pattern matching problem fall into this class. This research was primary done while the author was visiting INRIA, Rocquencourt, France, and he wishes to thank INRIA (projects ALGO, MEVAL and REFLECS) for a generous support. In addition, support was provided by NSF Grants CCR9201078, NCR9206315 and INT8912631, by Grant AFOSR900107, and in part by NATO Collaborative Grant 0057/89. 1. INTRODUCTION We co...
The Probability of Large Queue Lengths and Waiting Times in a Heterogeneous Multiserver Queue Part I: Tight Limits
, 1995
"... We consider a multiserver queuing process specified by i.i.d. interarrival time, batch size and service time sequences. In the case that different servers have different service time distributions we say the system is heterogeneous. In this paper we establish conditions for the queuing process to be ..."
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Cited by 10 (2 self)
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We consider a multiserver queuing process specified by i.i.d. interarrival time, batch size and service time sequences. In the case that different servers have different service time distributions we say the system is heterogeneous. In this paper we establish conditions for the queuing process to be characterized as a geometrically Harris recurrent Markov chain, and we characterize the stationary probabilities of large queue lengths and waiting times. The queue length is asymptotically geometric and the waiting time is asymptotically exponential. Our analysis is a generalization of the well known characterization of the GI/G/1 queue obtained using classical probabilistic techniques of exponential change of measure and renewal theory. American Mathematical Society subject classifications: Primary 60K25; Secondary 60F10, 60J05, 60K15, 60K20. Key Words: Queueing theory, Harris recurrent Markov chains, FosterLyapunov theory, Markov additive processes, renewal theory. 1 J. S. Sadowsky is...
Maximum Queue Length And Waiting Time Revisited: Multiserver GGc Queue
 Prob. Eng. Inf. Sci
, 1996
"... We characterize the probabilistic nature of the maximum queue length and the maximum waiting time in a multiserver GjGjc queue. We assume a general i.i.d. interarrival process and a general i.i.d. service time process for each server with the possibility of having different service time distribution ..."
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Cited by 7 (1 self)
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We characterize the probabilistic nature of the maximum queue length and the maximum waiting time in a multiserver GjGjc queue. We assume a general i.i.d. interarrival process and a general i.i.d. service time process for each server with the possibility of having different service time distributions for different servers. Under a weak additional condition we will prove that the maximum queue length and waiting time grow asymptotically in probability as log ! n \Gamma1 and log n 1=` , respectively, where ! ! 1 and ` ? 0 are parameters of the queueing system. Furthermore, it is shown that the maximum waiting time  when appropriately normalized  converges in distribution to the extreme distribution (x) = exp(\Gammae \Gammax ). The maximum queue length exhibits similar behavior, except that some oscillation caused by discrete nature of the queue length must be taken into account. The first results of this type were obtained for the GjM j1 queue by Heyde, and for the GjGj1 queue...