A call center is operated by a single operator and has room for at most three callers (including the call being serviced). Potential calls arrive at a Poisson rate of 4 per hour, and the successive service times are independent exponential random variables with mean 1/5 hour. (a) What is the average number of calls in the system? Draw the rate diagram, clearly defining the states and label all transition rates. (b) How many customers enter the system per hour? (c) If the operator could work twice as fast, how much more business would be done? (That is, on average, how many more customers would be able to enter the system per hour with respect to (b)?) Draw the rate diagram, clearly defining the states and labeling all transition rates. (d) Now, if the operator was working at the original rate of 4 customers per hour, but could hire an additional worker with the same service rate, how much more business would the call center do? (That is, on average, how many more customers would be able to enter the system per hour with respect to (b)?) Draw the rate diagram, clearly defining the states and labeling all transition rates.
A call center is operated by a single operator and has room for at most three callers (including the call being serviced). Potential calls arrive at a Poisson rate of 4 per hour, and the successive service times are independent exponential random variables with mean 1/5 hour. (a) What is the average number of calls in the system? Draw the rate diagram, clearly defining the states and label all transition rates. (b) How many customers enter the system per hour? (c) If the operator could work twice as fast, how much more business would be done? (That is, on average, how many more customers would be able to enter the system per hour with respect to (b)?) Draw the rate diagram, clearly defining the states and labeling all transition rates. (d) Now, if the operator was working at the original rate of 4 customers per hour, but could hire an additional worker with the same service rate, how much more business would the call center do? (That is, on average, how many more customers would be able to enter the system per hour with respect to (b)?) Draw the rate diagram, clearly defining the states and labeling all transition rates.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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A call center is operated by a single operator and has room for at most three callers
(including the call being serviced). Potential calls arrive at a Poisson rate of 4 per hour, and the
successive service times are independent exponential random variables with mean 1/5 hour.
(a) What is the average number of calls in the system? Draw the rate diagram, clearly
defining the states and label all transition rates.
(b) How many customers enter the system per hour?
(c) If the operator could work twice as fast, how much more business would be done? (That
is, on average, how many more customers would be able to enter the system per hour with respect
to (b)?) Draw the rate diagram, clearly defining the states and labeling all transition rates.
(d) Now, if the operator was working at the original rate of 4 customers per hour, but
could hire an additional worker with the same service rate, how much more business would the
call center do? (That is, on average, how many more customers would be able to enter the system
per hour with respect to (b)?) Draw the rate diagram, clearly defining the states and labeling all
transition rates.
(including the call being serviced). Potential calls arrive at a Poisson rate of 4 per hour, and the
successive service times are independent exponential random variables with mean 1/5 hour.
(a) What is the average number of calls in the system? Draw the rate diagram, clearly
defining the states and label all transition rates.
(b) How many customers enter the system per hour?
(c) If the operator could work twice as fast, how much more business would be done? (That
is, on average, how many more customers would be able to enter the system per hour with respect
to (b)?) Draw the rate diagram, clearly defining the states and labeling all transition rates.
(d) Now, if the operator was working at the original rate of 4 customers per hour, but
could hire an additional worker with the same service rate, how much more business would the
call center do? (That is, on average, how many more customers would be able to enter the system
per hour with respect to (b)?) Draw the rate diagram, clearly defining the states and labeling all
transition rates.
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Step 1: Average number of calls in a call center system with Poisson arrivals and exponential service times
VIEWStep 2: Arrival rate of customers in a call center system with Poisson arrivals and exponential service time
VIEWStep 3: Impact of increased service rate on call center system
VIEWStep 4: Impact of adding a worker on call center system with Poisson arrivals and exponential service times
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