QueueTheoryExample - 32 0.000002 0.0488 33 0.000001 0.0406 34 0.000000 0.0339 35 0.000000 0.0282 Mean Arrivals/Unit Time(� Utilization(U(also ρ Mean

Single Queue Common Case 10 0.8333333333 12 4.1666666667 5 Arrival Probability 0.4166666667 N Pr[N arrivals] Pr[N in System] Service Time 0.0833333333 0 0.004540% 16.6667% Total Time in System 0.5 1 0.045400% 13.8889% 2 0.227000% 11.5741% 3 0.756665% 9.6451% 4 1.891664% 8.0376% 5 3.783327% 6.6980% 6 6.305546% 5.5816% 7 9.007923% 4.6514% 8 11.259903% 3.8761% 9 12.511004% 3.2301% 10 12.511004% 2.6918% 11 11.373640% 2.2431% 12 9.478033% 1.8693% 13 7.290795% 1.5577% 14 5.207710% 1.2981% 15 3.471807% 1.0818% 16 2.169879% 0.9015% 17 1.276400% 0.7512% 18 0.709111% 0.6260% 19 0.373216% 0.5217% 20 0.186608% 0.4347% 21 0.088861% 0.3623% 22 0.040391% 0.3019% 23 0.017561% 0.2516% 24 0.007317% 0.2097% 25 0.002927% 0.1747% 26 0.001126% 0.1456% 27 0.000417% 0.1213% 28 0.000149% 0.1011% 29 0.000051% 0.0843% 30 0.000017% 0.0702% 31 0.000006% 0.0585%

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Unformatted text preview: 32 0.000002% 0.0488% 33 0.000001% 0.0406% 34 0.000000% 0.0339% 35 0.000000% 0.0282% Mean Arrivals/Unit Time (λ) Utilization (U) (also ρ) Mean Service Rate (μ) Mean Length of Queue (L q ) Total Population in System L = ρ + Lq Waiting Time in Queue (W q ) Single Queue Common Case 210 280 0.75 0.25 Population 2.25 0.75 3 Time 0.0107142857 0.0035714286 0.0142857143 Mean Arrivals/Unit Time (λ) Mean Service Rate (μ) Utilization (U or ρ ) Idle Time = P = (1-ρ ) = (1-U) Queue L q = ( λ 2 ) / ( μ * ( μ-λ )) Server (U or ρ ) Total L = L q + ρ Queue W q = L q / λ Server (1/ μ ) Total W = W q + (1/ μ )...
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