3325p11hs d waiting line

Where for x 0 1 2 3 4 0 px probability of x arrivals

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Unformatted text preview: = 0, 1, 2, 3, 4, … 0, P(x) = probability of x arrivals x= number of arrivals per unit of time λ= average arrival rate e= 2.7183 (which is the base of the natural logarithms) D–9 Poisson Distribution e-λ λ x x! Probability = P(x) = 0.02 – Probability 0.25 – 0.02 – Probability 0.25 – 0.15 – 0.10 – 0.15 – 0.10 – 0.05 – 0.05 – – – 0123456789 Distribution for λ = 2 Distribution x 0 1 2 3 4 5 6 7 8 9 10 11 x Distribution for λ = 4 Distribution D – 10 Waiting-Line Characteristics Limited or unlimited queue length Queue discipline - first-in, first-out (FIFO) is most common Other priority rules may be used in special circumstances D – 11 Service Characteristics Queuing system designs Single-channel system, multiple-channel system Single-phase system, multiphase system Service time distribution Constant service time Random service times, usually a negative exponential distribution D – 12 Queuing System Designs A family dentist’s office Queue Service Service facility facility Arrivals Departures after service Single-channel, single-phase system A McDonald’s dual window drive-through Queue Arrivals Phase 1 Phase service facility facility Phase 2 Phase service facility facility Departures after service Single-channel, multiphase system D – 13 Queuing System Designs Most bank and post office service windows Service Service facility facility Channel 1 Queue Arrivals Service Service facility facility Channel 2 Depart...
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