Finite-Source Queueing Systems and their Applications

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János Sztrik 2001/08/05 messages in the service facility at an arbitary time in terms of π0, too, as γ = Nλ π0 + Nλb ; 1 E = π0 + Nλb 1 − π0 E[T ] = Nb − λ � � 1 E[L] = N 1 − π0 + Nλb We can find π0 by analyzing a Markov chain of the queue size embedded at service completion times, or the method of supplementary variables can be applied to obtain P0. Finite-Source Queueing Systems and their Applications (17) (18) (19)
János Sztrik 2001/08/05 Asymptotic properties We can discuss some asymptotic properties of these performance measures without recourse to detailed analysis of the system state. When N is fixed, for λ ≈ 0 we have almos no congestion at the service facility, which means that π0 ≈ 1, P0 ≈ 1, γ ≈ Nλ, E ≈ 1, E[T ] ≈ b and E[L] ≈ Nλb. As λ → ∞, every message whose service has just been completed returns to the facility almost immediately. Therefore π0 → 0, P0 → 0, γ → 1/b, E → 0, E[T ] → Nb, E[L] → N. We note that E[T ] in (10) or (18) as a function of N has simple asymptotic forms. When N = 1 (which is equivalent to a loss system M/G/l/l), we 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
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Page 9 and 10: János Sztrik 2001/08/05 Example 3
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Page 13 and 14: János Sztrik 2001/08/05 Kendall no
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Page 25: János Sztrik 2001/08/05 will inclu
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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
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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)
Page 57 and 58: János Sztrik 2001/08/05 Setting s
Page 59 and 60: János Sztrik 2001/08/05 To get P
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Page 65 and 66: János Sztrik 2001/08/05 or P ∗ 1
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Page 75 and 76: 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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