The typical subway station in Toronto has six turnstiles, each of which can be controlled by the station supervisor to b

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The Typical Subway Station In Toronto Has Six Turnstiles Each Of Which Can Be Controlled By The Station Supervisor To B 1 (35.28 KiB) Viewed 31 times

The typical subway station in Toronto has six turnstiles, each of which can be controlled by the station supervisor to be used for either entrance or exit control — but never for both. The supervisor must decide at different times of the day how many turnstiles to use for entering passengers and how many to use for exiting passengers. At the Old Mill Station, passengers enter the station at a rate of about 84 per minute between the hours of 7 A.M. and 9 A.M. Passengers exiting trains at the stop reach the exit turnstile area at a rate of about 48 per minute during the same morning rush hours. Each turnstile can allow an average of 30 passengers per minute to enter or exit. Arrival and service times have been thought to follow Poisson and exponential distributions, respectively. Assume riders form a common queue at both entry and exit turnstile areas and proceed to the first empty turnstile. The Old Mill station supervisor, Ernie Forman, does not want the average passenger at his station to have to wait in a turnstile line for more than six seconds, nor does he want more than eight people in any queue at any average time.
a) How many turnstiles should be opened in each direction every morning? Fill in the table below (enter your responses rounded to two decimal places.) La 3 turnstiles for entering 4 turnstiles for entering 2.84 3.55 12.27 1.00 Wq (seconds) 8.77 0.71) 2 turnstiles for exiting 3 turnstiles for exiting 0.31 0.39 Out of the six turnstiles, for entering the station, 4 turnstiles should be used to meet the goals on queue length and the waiting time. (Enter your response as a whole number.) Out of the six turnstiles, for exiting the station, 2 turnstiles should be used to meet the goals on queue length and the waiting time. (Enter your response as a whole number.) b) Discuss the assumptions underlying the solution of this problem using queuing theory. What are the assumptions in a multichannel queuing model? Select all that apply. 「ロロロ O A. Arrivals come from an infinite, or very large, population. B. Service times follow the exponential distribution C. Arrivals are Poisson distributed. D. Servers each perform at their own individual speeds.