In response to the ongoing pandemic, a local restaurant has implemented social distancing measures, which include the closing its in person dining areas. In order to keep the business going, the restaurant will now rely on drive through lines to handle customer ordering and service. After implementing the new ordering system, management observes that customers arrive at the rate of 62 customers per hour. Under the current system the restaurant has only 5 servers with a total service rate of 70 customers/hour.
Q.1 : Given the description above, what is the average amount of time customers will wait in line under the current restaurant scenario? (round to closest integer)
Q.2. Now consider that the restaurant manager from above is wanting to reduce customer waiting times. In order for this , the manager decides to add another server bringing the total number of servers to 6 and the total service rate to 84 customer/hour. On average, how many customers will be waiting in the queue after the manager introduces this extra server? (round to closest integer) (average arrival remains 62/hour)
Q.3: Now consider that every sever on duty for the restaurant adds a constant 14 customer/hour to the total service rate of the restaurant. Given that the rate of arrivals for the restaurant remains constant at 82 customers/hour, plot (using R) the average amount of time customers will wait in line with various numbers of servers. The minimum servers that can be on duty is 7 and the maximum is 20. Display the plot as output.
Q.4.A: Based on your plot above, at what number of servers does the average customer wait time drop below 3 minutes?
Q.4.B: Based on your plot above, Describe the behavior of the chart and give some commentary about the relationship between the two variables. For example, is the chart increase or decreasing? What value does average wait time approach if we continue to add more and more servers (to infinity)?