A reduced-peak equivalence for queues with a mixture of light-tailed and heavy-tailed input flows

被引:6
|
作者
Borst, S
Zwart, B
机构
[1] CWI, NL-1090 GB Amsterdam, Netherlands
[2] Eindhoven Univ Technol, NL-5600 MB Eindhoven, Netherlands
关键词
fluid queues; heavy-tailed on periods; large deviations; queue length asymptotics;
D O I
10.1239/aap/1059486829
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We determine the exact large-buffer asymptotics for a mixture of light-tailed and heavy-tailed input flows. Earlier studies have found a 'reduced-load equivalence' in situations where the peak rate of the heavy-tailed flows plus the mean rate of the light-tailed flows is larger than the service rate. In that case, the workload is asymptotically equivalent to that in a reduced system, which consists of a certain 'dominant' subset of the heavy-tailed flows, with the service rate reduced by the mean rate of all other flows. In the present paper, we focus on the opposite case where the peak rate of the heavy-tailed flows plus the mean rate of the light-tailed flows is smaller than the service rate. Under mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a somewhat 'dual' reduced system, multiplied by a certain prefactor. The reduced system now consists of only the light-tailed flows, with the service rate reduced by the peak rate of the heavy-tailed flows. The prefactor represents the probability that the heavy-tailed flows have sent at their peak rate for more than a certain amount of time, which may be interpreted as the 'time to overflow' for the light-tailed flows in the reduced system. The results provide crucial insight into the typical overflow scenario.
引用
收藏
页码:793 / 805
页数:13
相关论文
共 50 条
  • [1] Generalized processor sharing with light-tailed and heavy-tailed input
    Borst, S
    Mandjes, M
    van Uitert, M
    [J]. IEEE-ACM TRANSACTIONS ON NETWORKING, 2003, 11 (05) : 821 - 834
  • [2] Delay-Optimal Scheduling for Heavy-Tailed and Light-Tailed Flows via Reinforcement Learning
    Guo, Mian
    Guan, Quansheng
    Chen, Weiqi
    Ji, Fei
    Peng, Zhiping
    [J]. PROCEEDINGS OF 2018 IEEE INTERNATIONAL CONFERENCE ON COMMUNICATION SYSTEMS (ICCS 2018), 2018, : 292 - 296
  • [3] Tails of random sums of a heavy-tailed number of light-tailed terms
    Robert, Christian Y.
    Segers, Johan
    [J]. INSURANCE MATHEMATICS & ECONOMICS, 2008, 43 (01): : 85 - 92
  • [4] Concentration bounds for CVaR estimation: The cases of light-tailed and heavy-tailed distributions
    Prashanth, L. A.
    Jagannathan, Krishna
    Kolla, Ravi Kumar
    [J]. INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 119, 2020, 119
  • [5] Estimation of extremes for heavy-tailed and light-tailed distributions in the presence of random censoring
    Worms, Julien
    Worms, Rym
    [J]. STATISTICS, 2021, 55 (05) : 979 - 1017
  • [6] Randomly Stopped Sums, Minima and Maxima for Heavy-Tailed and Light-Tailed Distributions
    Leipus, Remigijus
    Siaulys, Jonas
    Danilenko, Svetlana
    Karaseviciene, Jurate
    [J]. AXIOMS, 2024, 13 (06)
  • [7] Fluid queues with heavy-tailed M/G/∞ input
    Borst, S
    Zwart, B
    [J]. MATHEMATICS OF OPERATIONS RESEARCH, 2005, 30 (04) : 852 - 879
  • [8] Ruin under Light-Tailed or Moderately Heavy-Tailed Insurance Risks Interplayed with Financial Risks
    Yiqing Chen
    Jiajun Liu
    Yang Yang
    [J]. Methodology and Computing in Applied Probability, 2023, 25
  • [9] Ruin under Light-Tailed or Moderately Heavy-Tailed Insurance Risks Interplayed with Financial Risks
    Chen, Yiqing
    Liu, Jiajun
    Yang, Yang
    [J]. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2023, 25 (01)
  • [10] When Heavy-Tailed and Light-Tailed Flows Compete: The Response Time Tail Under Generalized Max-Weight Scheduling
    Nair, Jayakrishnan
    Jagannathan, Krishna
    Wierman, Adam
    [J]. IEEE-ACM TRANSACTIONS ON NETWORKING, 2016, 24 (02) : 982 - 995