Mary Smith, manager of the ABC Hotel, is considering how to restructure the front desk to reach an optimum level of staff efficiency (the utilization factor between 80% and 95% will be considered acceptable) and guest service expressed as an average waiting time in the line/queue (any plan resulting in the waiting time longer than 20 minutes is unacceptable). At present, the hotel has four clerks on duty, each with a separate waiting line, during the peak check-in time. Observation of arrivals during this time shows that an average of 60 guests arrive each hour(15 guests on average for each check-in line) and they follow a Poisson process. It takes an average of 3 minutes and 20 seconds for each front-desk clerk to register each guest (this and all other service times are exponentially distributed). Mary is considering a number of plans for improving guest service by reducing the length of time guests spend waiting in line. The first plan is to convert the current system into a single-line system. All guests could form a single waiting line to be served by whichever of the four clerks became available. This option would require sufficient lobby space for what could be a substantial queue. Mary, however, is hoping that only three clerks would be enough (with one common line in front of them). This would be her second plan. The third plan would designate one employee as a quick-service clerk for guests registering under corporate accounts, a market segment that fills about 25% of all occupied rooms. Because corporate guests are preregistered, their registration takes just 2.5 minutes. With these guests separated from the rest of the clientele, the average time for registering a typical guest would climb to 3 minutes and 45 seconds. Under Plan 3, Mary is considering two options: a) noncorporate guests would choose any of the remaining separate three lines. b) noncorporate guests would form one common line in front of the remaining three clerks. Hint: When a plan comprises two systems/options (e.g. one M/M/1 system plus one M/M/3 system), to arrive at the final characteristic for the entire plan (e.g. the final, aggregate, waiting time for the entire plan or the final, aggregate, utilization factor ρ), you have to calculate the weighted average of the two waiting times or of the two utilization factors. Only this way you can compare various plans involving different options. The weights are percentages of the clients selecting each system/option. The total of weights must be 1 (i.e., 100%). Determine the average amount of time (in minutes) that a guest spends waiting in the line under the current mode of operation and three other plans. Calculate the utilization factor ρ
Mary Smith, manager of the ABC Hotel, is considering how to restructure the front desk to reach an optimum level of staff efficiency (the utilization factor between 80% and 95% will be considered acceptable) and guest service expressed as an average waiting time in the line/queue (any plan resulting in the waiting time longer than 20 minutes is unacceptable).
At present, the hotel has four clerks on duty, each with a separate waiting line, during the peak check-in time. Observation of arrivals during this time shows that an average of 60 guests arrive each hour(15 guests on average for each check-in line) and they follow a Poisson process. It takes an average of 3 minutes and 20 seconds for each front-desk clerk to register each guest (this and all other service times are exponentially distributed). Mary is considering a number of plans for improving guest service by reducing the length of time guests spend waiting in line.
The first plan is to convert the current system into a single-line system. All guests could form a single waiting line to be served by whichever of the four clerks became available. This option would require sufficient lobby space for what could be a substantial queue.
Mary, however, is hoping that only three clerks would be enough (with one common line in front of them). This would be her second plan.
The third plan would designate one employee as a quick-service clerk for guests registering under corporate accounts, a market segment that fills about 25% of all occupied rooms. Because corporate guests are preregistered, their registration takes just 2.5 minutes. With these guests separated from the rest of the clientele, the average time for registering a typical guest would climb to 3 minutes and 45 seconds. Under Plan 3, Mary is considering two options:
a) noncorporate guests would choose any of the remaining separate three lines.
b) noncorporate guests would form one common line in front of the remaining three clerks.
Hint: When a plan comprises two systems/options (e.g. one M/M/1 system plus one M/M/3 system), to arrive at the final characteristic for the entire plan (e.g. the final, aggregate, waiting time for the entire plan or the final, aggregate, utilization factor ρ), you have to calculate the weighted average of the two waiting times or of the two utilization factors. Only this way you can compare various plans involving different options. The weights are percentages of the clients selecting each system/option. The total of weights must be 1 (i.e., 100%).
Determine the average amount of time (in minutes) that a guest spends waiting in the line under the current mode of operation and three other plans. Calculate the utilization factor ρ.
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