2. The pharmacist at Arnold Palmer Hospital, Wende Huehn-Brown, receives 13 requests for prescriptions each hour,...

2. The pharmacist at Arnold Palmer Hospital, Wende Huehn-Brown, receives 13 requests for prescriptions each hour, Poisson distributed. It takes her a mean time of 4 minutes to fill each, following a negative exponential distribution. Use the waiting-line table, Table D.5 (select the closest matching value) and Wq=Lq/λ, to answer these questions.

a. What is the average number of prescriptions in the queue?

b. How long will the average prescription spend in the queue?

c. Wende decides to hire a second pharmacist, Ajay Aggerwal, with whom she went to school and who operates at the same speed in filling prescriptions. How will the answers to parts (a) and (b) change? NOTES: Start by determining how many prescriptions are filled per hour. Use formula in Table D.3 for Wq (also included above).

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Answer:-

The Pharmacist receives 13 Request for prescription each hour

Hence, Mean Arrival Rate of prescription (Lambda) = 13 Request per hour=13/hr (Arrival is Poisson distributed)

It takes 4 Minutes to fill each, It means service rate (mu) = 4/minutes, Hence, Service Rate per Hour = 60/4 =15 per hour = 15/hr

Average traffic intensity or service utilization rate (rho) = Mean arrival rate/ Avg service rate =13/15= 0.86.

Hence, As the arrival rate of prescription is Poisson distributed and service rate follows is negative exponentially distribution, and Number of service channel (M)is one, as wende huenn-brown herself prescribe.

(a)

From the table, select the value corresponding to service utilization rate (Rho = Lambda/rho) and M = 1, which is 6.54

hence value of L^q, Length of the queue or Avg number of prescription in the queue = L_q= 6.54

(b)

Average time spent in the queue or time spent by average prescription in the queue = Avg Number of Prescription in the queue / Avg Arrival rate = L_q / (Lambda) = 6.54 / 13 = 0.50 hours or 0.50* 60 = 30 Minutes

(c)

Wende decides to hire a second pharmacist,Ajay aggerwal, who operates at the same speed as of wende

Now the No of service channel has been increased from 1 to 2 , Hence, M= 2

Now from the table, choose the value corresponding to M=2 and service utilization rate (Lamnda/rho) = 0.86, the value of Lq = 0.20

the value of (a) and (b) will change

New value of Average Number of prescription in the queue = Lq = 0.20

New value of Average time spend in the queue = Lq/ Average arrival rate = 0.20 /13 = 0.0153 hours or 0.0153*60 = 0.918 Minutes or 55.08 seconds

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genius_generous answered 1 year ago

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