Finite-Source Queueing Systems and their Applications

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János Sztrik 2001/08/05 customers, request, jobs ect staying at the service facility. This happens in the case of finite-source queueing systems . Let us consider some specific examples following in order of their appearance in practice, see for example [2, 12, 15, 33, 58, 77] Finite-Source Queueing Systems and their Applications
János Sztrik 2001/08/05 Example 1 Consider a set of N machines that operate independently of each other. After a random time they may break down and need repair by one or several operatives (repairmen) for a random time. The repair is carried out by a specific discipline and after having been served each machine renew his operation. It is assumed that the server can handle only one machine at a time. Besides the usual main characteristics in reliability theory we would like to know the distribution of the failre-free operation time of the whole system. Finite-Source Queueing Systems and their Applications
Page 1 and 2: Finite-Source Queueing Systems and
Page 3 and 4: János Sztrik 2001/08/05 Introducti
Page 5: János Sztrik 2001/08/05 distributi
Page 9 and 10: János Sztrik 2001/08/05 Example 3
Page 11 and 12: János Sztrik 2001/08/05 Kendall’
Page 13 and 14: János Sztrik 2001/08/05 Kendall no
Page 15 and 16: János Sztrik 2001/08/05 job that w
Page 17 and 18: János Sztrik 2001/08/05 probabilit
Page 19 and 20: János Sztrik 2001/08/05 in accorda
Page 21 and 22: János Sztrik 2001/08/05 Performanc
Page 23 and 24: János Sztrik 2001/08/05 Hence we h
Page 25 and 26: János Sztrik 2001/08/05 will inclu
Page 27 and 28: János Sztrik 2001/08/05 Asymptotic
Page 29 and 30: János Sztrik 2001/08/05 Heterogene
Page 31 and 32: János Sztrik 2001/08/05 throughput
Page 33 and 34: János Sztrik 2001/08/05 If P (i) d
Page 35 and 36: János Sztrik 2001/08/05 The main a
Page 37 and 38: János Sztrik 2001/08/05 distributi
Page 39 and 40: János Sztrik 2001/08/05 rates λn
Page 41 and 42: János Sztrik 2001/08/05 (N − n)
Page 43 and 44: János Sztrik 2001/08/05 E[L] = N +
Page 45 and 46: János Sztrik 2001/08/05 7. Mean wa
Page 47 and 48: János Sztrik 2001/08/05 ρ N r Us
Page 49 and 50: János Sztrik 2001/08/05 A recursiv
Page 51 and 52: János Sztrik 2001/08/05 The mathem
Page 53 and 54: János Sztrik 2001/08/05 � ∂
Page 55 and 56: János Sztrik 2001/08/05 Using (45)
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János Sztrik 2001/08/05 Setting s
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János Sztrik 2001/08/05 To get P
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János Sztrik 2001/08/05 Now from (
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János Sztrik 2001/08/05 Hence from
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János Sztrik 2001/08/05 or P ∗ 1
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János Sztrik 2001/08/05 Numerical
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János Sztrik 2001/08/05 H 2 (µ 1
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János Sztrik 2001/08/05 Finite-Sou
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János Sztrik 2001/08/05 N M E 10 D
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János Sztrik 2001/08/05 Preliminar
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János Sztrik 2001/08/05 〈αm〉,
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János Sztrik 2001/08/05 Theorem 1.
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János Sztrik 2001/08/05 The queuei
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János Sztrik 2001/08/05 i.e., the
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János Sztrik 2001/08/05 Proof. Let
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János Sztrik 2001/08/05 pε[(i1, i
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János Sztrik 2001/08/05 This agree
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János Sztrik 2001/08/05 (63),(64),
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János Sztrik 2001/08/05 substituti
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János Sztrik 2001/08/05 Consequent
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János Sztrik 2001/08/05 Performanc
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János Sztrik 2001/08/05 holding ti
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János Sztrik 2001/08/05 Mean delay
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János Sztrik 2001/08/05 Average nu
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János Sztrik 2001/08/05 Numerical
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János Sztrik 2001/08/05 N = 5 N =
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János Sztrik 2001/08/05 References
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János Sztrik 2001/08/05 [11] Bunda
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János Sztrik 2001/08/05 [23] Gelen
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János Sztrik 2001/08/05 [34] Haver
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János Sztrik 2001/08/05 [46] Koval
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János Sztrik 2001/08/05 [56] Scher
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János Sztrik 2001/08/05 [68] Sztri
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János Sztrik 2001/08/05 [79] Trive
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