Segmented Queue

Waiting Line Segmentation

The Dilemma: People are very dissatisfied when they have to wait too long in lines. Some possible outcomes of long lines:

• customers may wait a certain amount of time and then leave;

• customers may refuse to enter, and go somewhere else;

• customers may refuse to enter, and plan to return later;

• customers may hire someone to wait in line for them;

• in the event that customers have no choice (e.g., some government offices) they may simply wait as long as it takes to be served.

Clearly, the cost (real cost or opportunity cost) of waiting is not the same for all customers. The purpose of this assignment is to test the effects of a system where people may pay a premium to avoid long waits. These people might be individuals with high opportunity cost, i.e., they could earn a lot more money at their regular occupation during the time spent in line. They might be people for whom excessive waiting imposes a real cost, i.e., time lost at work. Alternatively, they might be people who, simply by virtue of their personalities, do not like to wait in line.

We begin by segmenting the customers into two groups: those who are willing to wait for service and those who are willing to pay a premium in order to avoid a long wait. (Of course, customer sensitivity to waiting is in reality on a continuum and the waiting customers can probably be segmented into any number of groups.)

Customers may be offered a choice: either

1. wait in the regular line along with everyone else, and have a longer wait, or

2. pay a premium in return for a guarantee of fast service, with a separate queue devoted to these customers.

This is not unlike some existing mail-order fulfillment systems in which customers are given the option of paying a premium for overnight (or two-day, etc.) delivery. Airlines do some of this with their “first class” or “business class” customers. Some benefits of the premium these preferential customers pay include faster check-in, boarding, deplaning, and luggage pick-up.

The System: In a certain government office, individuals arrive according to a Poisson process with an average arrival rate (lambda) of 23.25 people per hour. There are two clerks serving these people; an individual clerk works at an average rate of service (mu) of 11.75 people per hour; service rate is also Poisson distributed. This is an M/M/s waiting-line system and steady-state system performance measures -- such as average number of people waiting in the queue, average time spent waiting in queue, and average time spent altogether in the system -- are computable according to several analytical formulas. Thus the results (MOEs) of this system may be summarized as follows:

• Avg # in Q = 91.52

• Ave time in Q = 3.94 hours

• Ave time in system = 4.021 hours

Clearly, this is less than optimal and customers will not be very happy when faced with an average wait of nearly 4 hours for a service that takes about five minutes to complete.

Possible Solution: For an additional cost, say $30, people can be guaranteed that they will not have to wait too long for service. In fact, a separate service area will be made available to them. For the purpose of this example, suppose that between four and 20 per cent of all arrivals to this government office are willing to avail themselves of and pay for this faster service, depending on the size of the additional cost. These individuals go to the special service area (with its own waiting line) and are thus not part of the regular waiting-line system.

Suppose at a charge of $30, two people per hour avail themselves of this special service. Then, the income generated by the premium paid by these two customers is $60/hour or $480/day. This is not only sufficient to pay the salary of the additional clerk but also may in fact result in additional profits. In this example, one additional clerk is sufficient to handle the “priority” customers. Obviously, at lower charges, say $15, more customers will opt for the special service.

Simulate this alternative system using various cost alternatives to see what happens to the MOEs: