Queuing and Simulation (Coursework Sample)

Queuing and Simulation Name Institution Queuing and Simulation Bristowe, the manager of Phoenix Boutique Hotel Group (PBHG), a boutique hotel intends to maintain the customer holding time for a phone reservation system to at most two minutes. Bristowe had implemented a toll free customer care reservation system which is used to find the best reservation match in all of the Group’s property. This analysis seeks to solve a queuing problem using the simulation approach. Given in the problem are the incoming call distribution along with their associated probabilities, and the Service Time probability distribution. The Monte Carlo simulation technique which employs the use of random numbers and multiples of trial runs has been used (Thomopoulos, 2012). PBHG has 3 agents for the 6 a.m. to 2 p.m. call shift. The cumulative service rates of the three agents are given below; Table 1: Service Time Distribution Time to Process Customer Inquiries (Minutes) Probability 1 0.19 2 0.17 3 0.16 4 0.15 5 0.11 6 0.08 7 0.03 The incoming call distribution is also given in the table below; Table 2: Incoming Call Distribution Time Between Calls (Minutes) Probability 1 0.13 2 0.23 3 0.27 4 0.19 5 0.15 6 0.09 The first table can be used to determine the service rate and the second table can be used to determine the arrival rate. In coming up with a simulation model to solve a queuing problem, it is necessary that the Arrival Time, Service Start Time and Service End Times be determined (Borshchev, 2013). The arrival time is the time a customer enters into the system. It is not necessarily true that all the customers will be served as soon as they enter into the system and therefore the service start times may indicate a slight delay (Thomopoulos, 2012). The service end times indicate the time a service is completed given the service rate. The first step in solving this problem is determining the random number distribution. To do this the probability distributions are summed up to form a total of 1. Then the random number bands are allocated according to their widths which represents their upper and lower ranges. Next random numbers for the number of trial runs are generated using the standard random number tables, computer software or a spreadsheet package. In solving this problem, a spreadsheet package was used. The random numbers were therefore generated corresponding to the arrival time distributions and the service rate distributions. These generated random numbers were then paired against their position in the random number distribution and consequently the required arrival time and service rates were deduced. The arrival times and service rates thereby defined were then used to calculate the time in the system, Time on hold, and the time the server is idle. The time spent in the system represents the time spent in the queue as well as the time spent being served. Bristowe’s main aim was to ensure that the customers were not placed on hold for more than 2 minutes. From the attached spreadsheet document which detail the running of the described simulation trials for the first 15 customers in a day, the average Time a customer was on hold was 4.13 minutes. The average time the server is idle is about 0.87 minutes and this represents the time the customers are yet to arrive into the queue. By implication therefore, Bristowe needs to employ more people so as to bring down the average time a customer is on hold from 4.13 minutes to 2 minutes. In the second scenario it is mentioned that Bristowe and PBHG will be featured in a national travel magazine with wide coverage and this is bound to increase its reservation call system traffic to the following distribution; Table 3: Incoming Call Distribution Time Between Calls (Minutes) Probability 1 0.26 2 0.27 3 0.24 4 0.14 5 0.11 6 0.06 Assuming the current service rate and employing the same Monte Carlo simulation approach, the random number distributions were defined and a spreadsheet package was used to generate the random numbers. In the second scenario, the time on hold has increased to about 6.33 minutes. This therefore necessitates the increase in the number of call staff because the new time on hold is three times the desired length of holding time. Simulation analysis presents the following advantages; Simulation can be used to study behavior that is not mathematically possible to model. Secondly, the method does not necessarily have to follow any data distribution hence it can be employed in almost all scenarios, the simulation technique provides a very good training ground for future employees, and lastly the simulation technique maybe the only model available in the studying of particular problem...