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研究生:吳欣儒
研究生(外文):Sin-Ru Wu
論文名稱:藉由一位不可靠的服務員之等待系統刻劃指數分佈
論文名稱(外文):Some Characterizations of the Exponential Distribution related to a Single-server Queueing System with an Unreliable Server
指導教授:黃文璋黃文璋引用關係
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:8
中文關鍵詞:更新過程刻劃不可靠的服務員指數分佈
外文關鍵詞:characterizationrenewexponential distribution
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本文主要討論關於一位不可靠的服務員工作被中斷後,立刻重新工作的等待系統。針對此系統我們給定工作所需要的全部時間之變異數為常數來刻劃指數分佈。此結果可以視為一種指數分佈之無記憶性質。


Consider a single-server queueing system with an unreliable server and service repetition. In this system, if the service is interrupted, the service is restarted anew immediately and ends whenever the service period is failure free. In this paper, we give some characterization of the
exponential distribution by the constancy of total service time in this system. The result can be viewed as a kind of memoryless property of the exponential distribution.


Contents
1. Introduction..................................1
2. Preliminaries.................................3
3. Characterization based on variance............5
References.......................................7


1 Apostol, T. M.(1974). Mathematical Analysis, 2nd ed. Addison-Wesley, Reading, Massachusetts.2 Azlarov, T.A. and Volodin, N.A. (1986). Characterization Problems Associated with the Exponential Distribution (Translated by Stein, M. and Edited by Olkin, I.). Springer-Verlag, New York.3 Dimitrov, B. and Khalil, Z. (1990). On a new characterization of the exponential distribution related to a queueing system with an unreliable server. J. Appl. Prob. 27, 221-226.4 Galambos, J. and Kotz, S. (1978). Characterizations of Probability Distributions. { Lecture Notes in Mathematics} { f 675}, Springer-Verlag, New York.5 Huang, W.J. and Shoung, J.M. (1993). Some characterizations of the exponential and geometric distributions arising in a queueing system with an unreliable server. {it J. Appl. Prob.} { f 30}, 985-990.6 Huang, W.J., Li, S.H. and Su,J.C. (1993). Some characterizations of the Poisson process and geometric renewal process. {it J. Appl. Prob.} { f 30}, 121-130.7 Huang, W.J. and Chen, W.P. (1996). Some characterizations of the geometric distribution related to a single-server queueing system with an unreliable server. (in Chinese) {it J.C.S.A.} { f 34}, 275-287.8 Huang, W.J. and Chang, W.C. (2000). On a study of the exponential and Poisson characteristics of the Poisson process. {it Metrika} { f 50}, 247-254.9 Khalil, Z. and Dimitrov, B. (1994) The service time properties of an unreliable server characterize the exponential distribution. {it Adv. Appl. Prob.} { f 26}, 172-182.10 Khalil, Z., Dimitrov, B. and Dion, J.P. (1991) A characterization of the geometric distribution related to random sums. {it Commun. Statist.-Stoch. Models} { f 7}, 321-326.11 Lin, G.D. (1993). Characterizations of the exponential distribution via the blocking time in a queueing system. {it Statistica Sinica} { f 3}, 577-581.12 Ross, S.L. (1984). Differential Equations, 3rd ed. Wiley, New York.13 Silverman, R.A. (1974). Complex Analysis with Applications. Pren-tice-Hall, Inc., Englewood Cliffs, N. J.14 Simmons, G.F. (1991). Differential Equations with Applications and Historical Notes, 2nd ed. McGraw-Hill, New York.15 Van Harn, K. and Steutel, F.W. (1991). On a characterization of the exponential distribution. {it J. Appl. Prob.} { f 28}, 947-949.16 Xu, J.L. (1998) Characterization of the exponential distribution via the blocking time in a queueing system with an unreliable server. {it J. Appl. Prob.} { f 35}, 236-239.

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