4. Manhatten Snooze Pods installs 5 new “Z-time Sleep Pods” to their first city

Question

4. Manhatten Snooze Pods installs 5 new “Z-time Sleep Pods” to their first city location. Clients can stop by without an appointment on their work breaks for a relaxing snooze or quiet downtown during the work day. Clients who want to use these pods arrive at the rate of 12 per hour. The coefficient of variation of the inter-arrival times equals 2. If all three pods get busy, clients can relax in the front lounge drinking tea and reading a magazine, waiting for one of the pods to come available. The napping experience occurs in brief periods – 25 minutes of complete relaxation. The standard deviation of the usage times (measured in minutes) equals 4.

A?On average, how many Manhatten clients are using the snooze pod?

B?On average, how many Manhatten clients are waiting to use a snooze pod?

Explanation / Answer

b)

arrival rate 12 per hour interarrival time, a 5 min coefficient of variation of the inter-arrival times 2 Cva no. of pods, m 3 service period for 1 pod, p 25 min standard deviation of the service time 4 min CVp A?On average, how many Manhatten clients are using the snooze pod? mean no of customers in the service = utilization = p/ma No. of clients using snooze pods = 0.69 = 69%

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