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IIE Transactions Volume 39, 2007 - Issue 10

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ORIGINAL ARTICLES

Approximate mean waiting time in a GI/D/1 queue with autocorrelated times to failures

Bariş Balcio[gtilde]lu Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Rd., Toronto, ON M5S 3G8, Canada

David L. Jagerman RUTCOR, Rutgers University, 640 Bartholomew Rd., Piscataway, NJ, 08854, USA

Tayfur Altiok Department of Industrial and Systems Engineering, Rutgers University, 96 Frelinghuysen Rd., Piscataway, NJ, 08854, USA

Pages 985-996 | Received 01 Sep 2006, Accepted 01 Dec 2006, Published online: 26 Sep 2007

Cite this article
https://doi.org/10.1080/07408170701275343

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Fig. 1 The process completion random variable, C _m(x).

Table 1 Mean waiting times in M/D/1 systems with λ = 0.1, a TES⁺ times to failure process and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Display Table

Table 2 Mean waiting times in M/D/1 systems with λ = 0.119 76, a TES⁺ times to failure process and f _D(d) = Uniform(0.34, 0.5), with d ₁ = 0.42, d ₂ = 0.178 54, and a 20% down time

Display Table

Table 3 Mean waiting times in M/D/1 systems with λ = 0.1399, a TES⁺ times to failure process and f _D(d) = Uniform(0.1, 0.26), with d ₁ = 0.18, d ₂ = 0.034 54, and a 10% down time

Display Table

Table 4 Mean waiting times in M/D/1 systems with λ = 0.1, an MMPP times to failure process and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Display Table

Table 5 PH distributions approximating the PCT in the G/D/1 queue

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Table 6 Mean waiting times in GI/D/1 systems with GE(0.2, 1,2) interarrival times with c ² _A = 0.5, TES⁺ times to failure and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Display Table

Table 7 Mean waiting times in GI/D/1 systems with H2(0.888 89, 0.2, 0.02) interarrival times with c ² _A = 5, TES⁺ times to failure and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Display Table

Table 8 Mean waiting times in GI/D/1 systems with GE(0.2, 1,2) interarrival times with c ² _A = 0.5, MMPP times to failure and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Display Table

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Approximate mean waiting time in a GI/D/1 queue with autocorrelated times to failures

Table 1 Mean waiting times in M/D/1 systems with λ = 0.1, a TES⁺ times to failure process and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Table 2 Mean waiting times in M/D/1 systems with λ = 0.119 76, a TES⁺ times to failure process and f _D(d) = Uniform(0.34, 0.5), with d ₁ = 0.42, d ₂ = 0.178 54, and a 20% down time

Table 3 Mean waiting times in M/D/1 systems with λ = 0.1399, a TES⁺ times to failure process and f _D(d) = Uniform(0.1, 0.26), with d ₁ = 0.18, d ₂ = 0.034 54, and a 10% down time

Table 4 Mean waiting times in M/D/1 systems with λ = 0.1, an MMPP times to failure process and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Table 5 PH distributions approximating the PCT in the G/D/1 queue

Table 6 Mean waiting times in GI/D/1 systems with GE(0.2, 1,2) interarrival times with c ² _A = 0.5, TES⁺ times to failure and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Table 7 Mean waiting times in GI/D/1 systems with H2(0.888 89, 0.2, 0.02) interarrival times with c ² _A = 5, TES⁺ times to failure and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Table 8 Mean waiting times in GI/D/1 systems with GE(0.2, 1,2) interarrival times with c ² _A = 0.5, MMPP times to failure and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

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Approximate mean waiting time in a GI/D/1 queue with autocorrelated times to failures

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Table 1 Mean waiting times in M/D/1 systems with λ = 0.1, a TES+ times to failure process and f D(d) = Uniform(0.5, 1), with d 1 = 0.75, d 2 = 0.5833, and a 30% down time

Table 2 Mean waiting times in M/D/1 systems with λ = 0.119 76, a TES+ times to failure process and f D(d) = Uniform(0.34, 0.5), with d 1 = 0.42, d 2 = 0.178 54, and a 20% down time

Table 3 Mean waiting times in M/D/1 systems with λ = 0.1399, a TES+ times to failure process and f D(d) = Uniform(0.1, 0.26), with d 1 = 0.18, d 2 = 0.034 54, and a 10% down time

Table 4 Mean waiting times in M/D/1 systems with λ = 0.1, an MMPP times to failure process and f D(d) = Uniform(0.5, 1), with d 1 = 0.75, d 2 = 0.5833, and a 30% down time

Table 5 PH distributions approximating the PCT in the G/D/1 queue

Table 6 Mean waiting times in GI/D/1 systems with GE(0.2, 1,2) interarrival times with c 2 A = 0.5, TES+ times to failure and f D(d) = Uniform(0.5, 1), with d 1 = 0.75, d 2 = 0.5833, and a 30% down time

Table 7 Mean waiting times in GI/D/1 systems with H2(0.888 89, 0.2, 0.02) interarrival times with c 2 A = 5, TES+ times to failure and f D(d) = Uniform(0.5, 1), with d 1 = 0.75, d 2 = 0.5833, and a 30% down time

Table 8 Mean waiting times in GI/D/1 systems with GE(0.2, 1,2) interarrival times with c 2 A = 0.5, MMPP times to failure and f D(d) = Uniform(0.5, 1), with d 1 = 0.75, d 2 = 0.5833, and a 30% down time

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Table 1 Mean waiting times in M/D/1 systems with λ = 0.1, a TES⁺ times to failure process and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Table 2 Mean waiting times in M/D/1 systems with λ = 0.119 76, a TES⁺ times to failure process and f _D(d) = Uniform(0.34, 0.5), with d ₁ = 0.42, d ₂ = 0.178 54, and a 20% down time

Table 3 Mean waiting times in M/D/1 systems with λ = 0.1399, a TES⁺ times to failure process and f _D(d) = Uniform(0.1, 0.26), with d ₁ = 0.18, d ₂ = 0.034 54, and a 10% down time

Table 4 Mean waiting times in M/D/1 systems with λ = 0.1, an MMPP times to failure process and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Table 6 Mean waiting times in GI/D/1 systems with GE(0.2, 1,2) interarrival times with c ² _A = 0.5, TES⁺ times to failure and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Table 7 Mean waiting times in GI/D/1 systems with H2(0.888 89, 0.2, 0.02) interarrival times with c ² _A = 5, TES⁺ times to failure and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time

Table 8 Mean waiting times in GI/D/1 systems with GE(0.2, 1,2) interarrival times with c ² _A = 0.5, MMPP times to failure and f _D(d) = Uniform(0.5, 1), with d ₁ = 0.75, d ₂ = 0.5833, and a 30% down time