email: title: Queuing Analysis Queuing analysis is the study of waiting lines, and the goal of queuing analysis is to minimize total costs of a business; that is, to minimize both the costs of maintaining the ability of providing service (i. e. cashiers in a supermarket), and the costs of customer waiting. Much of the success of a particular store, or restaurant can depend upon choosing the correct queuing model to minimize these costs. A queuing model for a particular business is chosen based upon four characteristics of the business’s ystem: the population source, the number of servers, arrival and service patterns, and the queue discipline (order of service).
Population source describes the source from which a business draws its potential customers.
As opposed to a finite source, in which the number of customers is limited, Leo’s Deli has an infinite source population. Their number of customers is potentially unlimited. Though it would be highly unlikely to happen, every member of the calling population (every student, faculty, and staff member of the school) can go to Leo’s and request service at one time. The number of servers refers to the number of people serving customers at a given time. For our purposes, servers working together as a team are counted together as one server. At Leo’s Deli, a team of a cashier, sandwich maker, and a wrapper will be counted as one server.
For peak times, Leo’s utilizes a two lines, two server system. There is a separate line for each server. During non-peak times, Leo’s uses a one line, one server system. Waiting lines are a direct result of variability in customer arrival patterns. At some times, workers can be idle due to low arrivals, while at other times, the system can be overloaded due to bunched arrivals. Lines are most likely to occur when arrivals are bunched together, or when service times are particularly lengthy.
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For Leo’s Deli the arrival rate is generally up during a 20-minute time frame right after the end of a class period. As for the queue discipline, Leo’s Deli employs a “first-come, first-served” philosophy. As stated before, Leo’s utilizes a two server / two line system during peak times. Peak times are defined as between 11 am and about 2 pm, with the busiest times between 12 p-1: 30 p.
During non-peak times, or on slow days, there is a one line / one server system. To describe their operations, a customer joins one of the lines, and waits in line until he gets to a cashier. There is no jockeying between lines, as there is a divider between the lines. Their order is taken, and the customer pays for his order. The customer then waits as the sandwich maker prepares his order.
The finished sandwich is given to a wrapper, who slices and wraps the sandwich, and gives it to the customer, who then leaves. Upon analysis of Leo’s over a four-day period during peak times, it was found that the average arrival rate is approximately 48 customers / hr . during peak time (approximately 4 customers every 5 minutes).
Of course, this is for the whole kiosk (both lines combined), so the average arrival rate for each line is approximately 24 customers / hr . For our purposes, the time spent in line is defined as the time a customer joins the line, until the time he tells the cashier his order. The average time spent in line for each customer is about 1 m 30 s.
It was found that this is independent of whether there is one line or two. Consequently, the service time is defined as the time the cashier takes an order, until the time the customer leaves the kiosk. The average service time was found to be about 2 minutes. A summary of all queuing rates and times appears below. Queuing Analysis for Leo’s Deli (Between 12 p-2 p) KEY: l = Arrival rate – The rate at which customers arrive, and enter the system at Leo ” sm = Service rate – The rate at which a server / team can serve customers Lq = no.
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of customers in lines = no. of customers in whole system Wq = amount of time customer waits in lines = amount of time customer waits in whole system (both lines) = 48 customers / hr . l (one line) = 24 customers / hr . m = 30 customers / hr . (All subsequent calculations are per 1 line) Lq = 3. 2 customer sLs = 4 customers Wq (observed) = .
025 hrs Wq (calculated) = 0. 13 hr sWs (calculated) = . 166 hrs During the queuing analysis of Leo’s Delancy Street Deli, there were a couple of observations. First, customers tend to joining one line, so at times the kiosk turns into a one line, 2 server model. This situation is usually remedied quickly by the staff, as they make customers aware of the second line. Second, there is a large discrepancy between the observed time spent in line (1 m 30 s), and the calculated time spent in line (6 m).
The reason for this is currently unknown.
