• Title/Summary/Keyword: stationary distribution

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Stationary Distribution for the Mobilities in Catastrophe Rescue Scenario

  • Wang, Yong;Peng, Wei;Dou, Qiang;Gong, Zhenghu
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.7 no.2
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    • pp.308-326
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    • 2013
  • Mobility Model has drawn more and more attentions since its critical role in Mobile Wireless Networks performance evaluation. This paper analyzes the mobility patterns in the catastrophe rescue scenario, and proposes the Random Waypoint with Base Point mobility model to model these characteristics. We mathematically analyze the speed and spatial stationary distributions of the nodes and derive explicit expressions for the one dimensional case. In order to keep the stationary distribution through the entire simulation procedure, we provide strategies to initialize the speed, location and destination of the nodes at the beginning of the simulation. The simulation results verify the derivations and the proposed methods in this paper. This work gives a deep understanding of the properties of the Random Waypoint with Base Point mobility model and such understanding is necessary to avoid misinterpretation of the simulation results. The conclusions are of practical value for performance analysis of mobile wireless networks, especially for the catastrophe rescue scenario.

Designing an Algorithm for the Priority Deciding and Recommending of the Logistic Support with Stationary Distribution (Stationary 분포를 이용한 군수지원 우선순위 결정 및 추천 알고리즘 설계)

  • Noh, Giseop;Jeong, Sihyun;Kim, Chong-Kwon;Oh, Hayoung
    • Journal of KIISE
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    • v.41 no.12
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    • pp.1075-1080
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    • 2014
  • One of the important roles used to ensure victory in a war is to maximize the overall military forces and to make sure that the capability of the military forces can be sustained as much as possible. Although several researchers have proposed various possible methodologies for logistics support, no research trials have been undertaken to investigate logistics support that considers all relevant elements of such. Unlike previous in trials that consider and analyze the system fault ratio as the main methodology, we propose an approach that simultaneously decides and recommends logistic priority by reflecting and combining item costs, transportation, fault-ratio, and system complexity. Also, we designed an algorithm that can recommend optimized logistics support priority using stationary distribution.

An M/G/1 queue under the $P_{\lambda,\tau}^M$ service policy

  • Kim, Jong-Woo;Lee, Ji-Yeon
    • 한국데이터정보과학회:학술대회논문집
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    • 2005.04a
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    • pp.25-29
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    • 2005
  • We analyze an M/G/1 queueing system under $P_{\lambda,\tau}^M$ service policy. By using the level crossing theory and solving the corresponding integral equations, we obtain the stationary distribution of the workload in the system explicitly.

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BMAP/M/N/O Queueing System in Random Environments

  • Kim, Che-Soong
    • Proceedings of the Korean Society for Quality Management Conference
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    • 2007.04a
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    • pp.461-465
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    • 2007
  • The BMAP/M/N/O queueing system operating in Markovian random environment is investigated. The stationary distribution of the system is calculated. Loss probability and other performance measures are calculated. Numerical experiments which show the necessity of taking into account the influence of random environment and correlation in input flow are presented.

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A Renewal Theorem for Random Walks with Time Stationary Random Distribution Function

  • Hong, Dug-Hun
    • Journal of the Korean Statistical Society
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    • v.25 no.1
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    • pp.153-159
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    • 1996
  • Sums of independent random variables $S_n = X_1 + X_ + cdots + X_n$ are considered, where the X$_{n}$ are chosen according to a stationary process of distributions. Given the time t .geq. O, let N (t) be the number of indices n for which O < $S_n$ $\geq$ t. In this set up we prove that N (t)/t converges almost surely and in $L^1$ as t longrightarrow $\infty$, which generalizes classical renewal theorem.m.

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An M/G/1 Queue under the $P_\lambda\;^M$ with a Setup Time

  • Lee Jiyeon;Kim Jongwoo
    • Proceedings of the Korean Statistical Society Conference
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    • 2004.11a
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    • pp.301-306
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    • 2004
  • We consider the $P_\lambda\;^M$ service policy for an M/G/1 queue in which the service rate is increased from 1 to M at the exponential setup time after the level of workload exceeds $\lambda$. The stationary distribution of the workload is explicitly obtained through the level crossing argument.

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D-MAP 도착과정을 갖는 이산시간 대기행렬모형에서의 분포적 Little의 법칙과 D-MAP/D/c 모형에의 응용

  • Kim Nam-Gi
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2006.05a
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    • pp.1101-1103
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    • 2006
  • For a broad class of discrete-time FIFO queueing systems with D-MAP (discrete-time Markovian arrival process) arrivals, we present a distributional Little's law that relates the distribution of the stationary number of customers in system (queue) with that of the stationary number of slots a customer spends in system (queue). Taking the multi-server D-MAP/D/c queue for example, we illustrate how to utilize this relation to get the desired distribution of the number of customers.

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A New Approach to an Inventory with Constant Demand

  • Lee, Eui-Yong
    • Journal of the Korean Data and Information Science Society
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    • v.19 no.4
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    • pp.1345-1352
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    • 2008
  • An inventory with constant demand is studied. We adopt a renewal argument to obtain the transient and stationary distribution of the level of the inventory. We show that the stationary distribution can be also derived by making use of either the level crossing technique or the renewal reward theorem. After assigning several managing costs to the inventory, we calculate the long-run average cost per unit time. A numerical example is illustrated to show how we optimize the inventory.

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Analysis of BMAP/M/N/0 Queueing System for Telecommunication Network Traffic Control (통신망 트래픽 제어를 위한 BMAP/M/N/0 대기행렬모형 분석)

  • Lee, Seok-Jun;Kim, Che-Soong
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.30 no.4
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    • pp.39-45
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    • 2007
  • The BMAP/M/N/0 queueing system operating in Markovian random environment is investigated. The stationary distribution of the system is derived. Loss probability and other performance measures of the system also are calculated. Numerical experiments which show the necessity of taking into account the influence of random environment and correlation in input flow are presented.

WEAK CONVERGENCE FOR INTERATED RANDOM MAPS

  • Lee, Oe-Sook
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.485-490
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    • 1998
  • We consider a class of discrete parameter processes on a locally compact Polish space $S$ arising from successive compositions of strictly stationary Markov random maps on $S$ into itself. Sufficient conditions for the existence of the stationary solution and the weak convergence of the distributions of $\{\Gamma_n \Gamma_{n-1} \cdots \Gamma_0x \}$ are given.

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