1. A bank with five tellers opens its doors at 9 AM and closes its doors at 5 PM, but it operates until all customers in the bank by 5 PM have been served. Assume that the interarrival times of customers are exponentially distributed with a mean of 1 min and that the service times of customers are exponentially distributed with a mean of 4.5 min. In the current configuration, each teller has a separate queue (see. Figure 8.64). An arriving customer joins the shortest queue, choosing the shortest queue furthest to the left in case of ties.
Figure: Teller configuration (Multiple queues)
The bank's management team is concerned with operating costs as well as the quality of service currently being provided to customers, and they are thinking about changing the system to a single queue. In the proposed system, all arriving customers would join a single queue. In the first customer in t ho queue goes to the first available teller. Simulate 5 days of operation of the current and proposed systems
2. Airline ticket counter-At an airline ticket counter, the current practice is to allow queues to form before each ticket agent. Time between arrivals to the agents is exponentially distributed with a mean of 5 min. Customers join the shortest queue at the time of their arrival. The service time for the ticket agents is uniformly distributed between 2 and 10 min:
a. Develop an ExtendSim model to determine the minimum number of agents that will result in an average waiting time of 5 min or loss.
b. The airline has decided to change the procedure involved in processing Customers by the ticket agents. A single line is formed, and customers are routed to the ticket agent who becomes free next.
3. Grocery store-You are hired by Safeway to help them build a number of simulation models to better understand the customer flows and queuing processes in a grocery store setting. The pilot project at hand focuses on an off-peak setting where at most two checkouts are open. To better understand the necessary level of detail and the complexities involved, Safeway wants a whole battery of increasingly more realistic and complex models. For each model, Safeway wants to keep track of (i.e., plot) the average cycle time, queue length, and waiting time in the queues To understand the variability, they also want to see the standard deviation of these three metrics. In addition, they would like to track the maximum waiting time and the maximum number of customers in line. Furthermore, to better understand the system dynamics, plots of the actual queue lengths over time are required features of the model. The off-peak setting is valid for about 4 h, so it is reasonable to run the simulation for 240 min. Furthermore, to facilitate an easier first-cut comparison between the models, a fixed random seed is recommended. Because Safeway plans to use these different models later, it is important that each model sheet has a limit of one model:
a. In the first model, your Only interest is the queues building up at the checkout counters. Empirical investigation has indicated that it is reasonable to model the arrival process (to the checkout counters) as a Poisson process with a constant arrival intensity of three customers per minute. The service time in a checkout station is on average 30 s per customer and will, in this initial model, be considered constant. Inspired by the successes of a local bank, Safeway wants to model a situation with one single line to both checkout counters. As soon as a checkout is available, the first person in the queue will go to this counter. After the customers have paid for their goods, they immediately leave the store.
b. Upon Closer investigation, it is 'clear that the-service time is not Constant but rather normally distributed with mean r 30 s and standard deviation r 10 s. What is the effect of the additional variability compared to the results in part (a)?
c. To be able to analyze the Of feet of different queuing Configurations, Safeway wants a model in which each checkout counter has its own queue. When a customer arrives to the checkout point, he or she will choose the shortest line. The customer is not allowed to switch queues after making the initial choice. Can you see any differences in system performance compared to the results in part (b)?
d. to make the model more realistic, Safeway also -wants to include the time customers spend in the store walking around and picking up their groceries. Empirical investigation has shown that there are basically two types of customers, and they need to be treated somewhat diffrently.
Type I: the light shopper who buys only a few items (fewer than 15)
- About 60% of the customers arriving to the store.
- the shopping time follows a triangular distribution with a most likely value of 5 min, a minimum value of 2 min, and a maximum value of 8 min.
- the service times for these customers at the checkout counter are exponentially distributed with a mean of 15 s.