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# 320a3 - STATS 320 Applied Stochastic Modelling Assignment 3...

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STATS 320 Applied Stochastic Modelling Assignment 3 Due 4 pm, Monday May 18, 2009 1 Patients arrive at an emergency clinic as a Poisson process at rate 5 per hour. The clinic is staffed by one doctor, and a consultation takes a period of time that is uniformly distributed on the interval [5 , 15) minutes. All interarrival times and service times are independent of one another. The queueing discipline is first come first served, and you may assume that the queue is operating in steady state. a Describe this queue using the Kendall A | S | m | n notation. b Determine the following quantities: i L , the expected number of patients at the clinic (including those being seen by the doctor) in steady state ii L q , the expected number of patients in the waiting room, waiting to see the doctor, in steady state iii L s , the expected number of patients being seen by the doctor, in steady state. iv W , W q and W s . c What is the expected length of a busy period for the doctor? (A busy period commences when a patient arrives after an idle period, and finishes when the doctor is next idle again.)

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320a3 - STATS 320 Applied Stochastic Modelling Assignment 3...

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