Question

In: Operations Management

The reservation office for Central Airlines has two agents answering incoming phone calls for flight reservations....

The reservation office for Central Airlines has two agents answering incoming phone calls for flight reservations. A caller can be put on hold until one of the agents is available to take the call. If all three phone lines (both agent lines and the hold line) are busy, a potential customer gets a busy signal, in which case the call is lost. All calls occur randomly (i.e., according to a Poisson process) at a mean rate of 15 per hour. The length of a telephone conversation has an exponential distribution with a mean of 4 minutes.

(a)Construct the rate diagram for this queueing system.

(b) Find the steady-state probability that:

(i) A caller will get to talk to an agent immediately.

(ii) The caller will be put on hold, and

(iii) The caller will get a busy signal.

Solutions

Expert Solution

keosha answered 1 year ago
Next > < Previous

Related Solutions

The reservation office for Central Airlines has two agents answering incoming phone calls for flight reservations....
The reservation office for Central Airlines has two agents answering incoming phone calls for flight reservations. A caller can be put on hold until one of the agents is available to take the call. If all three phone lines (both agent lines and the hold line) are busy, a potential customer gets a busy signal, in which case the call is lost. All calls occur randomly (i.e., according to a Poisson process) at a mean rate of 15 per hour....
Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional...
Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. a. Compute the probability of receiving one call in a 5-minute interval of time.   (to 4 decimals) b. Compute the probability of receiving exactly 13 calls in 15 minutes.   (to 4 decimals) c. Suppose no calls are currently on hold. If the agent takes 10 minutes to complete the current call, how many callers do you expect to be waiting by that time?...
Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional...
Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. a. Compute the probability of receiving four calls in a 5-minute interval of time. b. Compute the probability of receiving exactly 9 calls in 15 minutes. c. Suppose, no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time? d. Suppose, no calls are currently...
Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.
Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.a.Compute the probability of receiving one call in a 10 -minute interval of time.b.Compute the probability of receiving exactly11 calls in 15 minutes.c.Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time?What is the probability that none will be waiting?d. If no calls are...
Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 A.M...
Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 A.M to 11:00 A.M time period, calls to the reservation agent occur randomly at an average of one call every 3.75 minutes. Historical service time data show that a reservation agent spends an average of 3 minutes with each customer. The waiting line model assumptions of Poisson arrivals and exponential service times appear reasonable for the telephone reservation system. Regional Airlines’ management believes that offering...
Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 AM...
Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 AM to 2:00 PM time period, calls to the reservation agent occur randomly at an average rate of one call every 3.75 minutes. Historical service time data show that a reservation agent spends an average of 3 minutes with each customer. The waiting line model assumptions of Poisson arrivals and exponential service times appear reasonable for the telephone reservation system. At a planning meeting, Regional’s...
Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 AM...
Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 AM to 2:00 PM time period, calls to the reservation agent occur randomly at an average rate of one call every 3.75 minutes. Historical service time data show that a reservation agent spends an average of 3 minutes with each customer. The waiting line model assumptions of Poisson arrivals and exponential service times appear reasonable for the telephone reservation system. Regional Airlines management believes that...
The number of telephone calls coming into the central switchboard of an office building follows a...
The number of telephone calls coming into the central switchboard of an office building follows a Poisson process with an average of 4 calls per minute. a) What is the probability that at least 3 calls will arrive in a given one minute period? b) What is the probability that at least 20 calls will arrive in a given five minute period? c) What is the probability that the time from the opening of the switchboard until the first call...
The number of telephone calls coming into the central switchboard of an office building follows a...
The number of telephone calls coming into the central switchboard of an office building follows a Poisson process with an average of 4 calls per minute. a) What is the probability that at least 3 calls will arrive in a given one minute period? b) What is the probability that at least 20 calls will arrive in a given five minute period? c) What is the probability that the time from the opening of the switchboard until the first call...
South Central Airlines (SCA) operates a commuter flight between Atlanta and Charlotte. The regional jet holds...
South Central Airlines (SCA) operates a commuter flight between Atlanta and Charlotte. The regional jet holds 50 passengers, and currently SCA only books up to 50 reservations. Past data show that SCA always sells all 50 reservations, but on average, two passengers do not show up for the flight. As a result, with 50 reservations the flight is often being flown with empty seats. To capture additional profit, SCA is considering an overbooking strategy in which they would accept 52...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT