The following letter appeared in the Washington Post on Sunday, January 28, 1979:

Bunched- Up Buses
I have long been trying to discover why Metro buses on Wisconsin Avenue are regularly bunched during rush hours instead of being evenly spaced. It is a common experience to wait for 10 or 15 minutes in rain or snow, and then find three or four buses coming along together nose to tail.

As Metro refuses to reply to letters on this subject, I can only assume that it has something to bide. From the passenger's point of view, the advantages of even spacing are obvious-shorter waits and buses that are evenly filled, instead of being packed up at the front and half-empty behind. Traffic congestion is also eased. Evidently, either the company or its drivers must prefer bunching. I continue to wonder why.


This letter is typical of similar letters on this subject that invariably appear several times each year in our major newspapers. The phenomenon is often referred to as the "clumping" or "bunching" of urban buses and is among the most irritating in the daily experiences of many of us. If the key performance measure of a bus transit system is curbside wait, then clumped buses can increase mean curbside wait by a factor of 2 or more compared to a system with evenly spaced buses. In effect, a system of buses clumped in pairs can reduce a system of N buses, each having capacity C, to a system with N12 "macro buses," each having capacity 2C. It is apparent that a study to decrease clumping and hence curbside waits can, in effect, substitute for the number of additional buses that would have been necessary under old operating procedures to achieve the same curbside-wait reduction. Many such studies can be extremely cost-effective according to the curbside-wait measure. Dissatisfaction with urban service provision is not limited to buses. In the late 1960s, citizens complained in letters to the editor of the New York Times of incurring delays in excess of 20 minutes prior to the answering of New York's (then new) 911 emergency telephone number. Other complaints span the spectrum of urban services, from negligence in pothole repair, to late arrival of emergency medical services, to slow removal of snow from the streets. In the remainder of this section we provide thumbnail sketches of deployment problems that are particularly well suited to an urban operations research approach. However, we do not wish to deceive the reader with the apparent simplicity of these problems; implementation of any proposed approach is a difficult process, requiring sensitivity to many of the issues raised in Chapter 8.

Example1: Value of (Partial) Information on Vehicle Location

The Bonded Taxi Company has been losing revenue recently because of the overambitiousness of some of its own drivers. The radio dispatcher usually assigns that cab which claims to be closest to the scene of a call for cab service. However, some of the more ambitious drivers have been claiming to be "right around the block," when actually they might be at a distant location. Such a car takes a long time to reach the scene; upon arrival, the driver finds either a very dissatisfied customer who will never again use Bonded or no customer at all (because the customer called another cab company).

The Urbtronics Corporation has offered to sell Bonded a .1-mile-resolution car-locator system, which, it is claimed, would provide the dispatcher with accurate position information, thereby eliminating distant dispatches caused by overly ambitious drivers. Other advantages of the car-locator system would include safety to drivers and better tracking of actual passenger mileage.

You have been hired to evaluate the advantages (and disadvantages) of the car-locator system. What do you do?

Example 2: Location of Garbage Incinerators

A mayor of a large city has discovered, to his surprise and consternation, that the city's refuse-collection trucks spend more time every day in moving back and forth between the city and a few remote garbage dumping sites that the city uses than in collecting garbage from city streets. It has been decided that several environmentally safe garbage incinerators will be built at a number of isolated locations within the city's boundaries, so that travel distances for unloading garbage can be reduced drastically. About 10 potential (and politically feasible) sites have been identified. The following interrelated questions must now be answered:
a. How many incinerators should be built?
b. Where, among the available sites, should the incinerators be located?
c. Which "truck runs" should be assigned to which incinerator?

Example 3: School-Bus Routing

For many suburban communities, especially those with relatively low population densities, the cost of transporting students to and from the community schools represents an important fraction of the annual school budget. In a large number of these cases the design of bus routes has been made on a haphazard basis with new bus stops and routes added as new children entered the school system. It is often possible to find instances where two or more different buses make stops at the same location to pick up different sets of students attending the same school. An additional problem is that, because of inefficient route design, some students are transported to school much before class time, thus increasing the need for the presence of supervisors at the schools, for additional recreational facilities, and so on.

An improved route-design process would offer the dual benefit of (1) reducing the number of bus runs and transportation costs, and (2) improving the quality of service to the students. Can such a process be devised?

Example 4: Relocation Strategies for Fire Companies

Although the average utilization of firemen is less than 25 percent in a particular city, the city is still experiencing unusually long delays in reaching some serious fires. These occur because demand patterns peak between 7: 00 P.m. and 9: 00 P.m., and one large fire (or several smaller ones, or false alarms) can "clean out" the fire stations in an area. The department has previously allowed dispatchers to move up (or relocate, reposition) certain companies. But with current levels of congestion they cannot adequately perform this task, because of heavy peak workloads and a lack of quantitative guidelines on how the relocation is to be done.

You are working for SOLVEIT Consulting Associates. You have been hired by the fire department to devise improved relocating strategies. A real-time computer capability is being implemented by the department and you have the freedom to use the computer in your system design. Design an approach and a solution method for this problem.

Example 5: Effects of a Law on Police Tours of Duty

Since the state legislature passed the "three-tour statute" in 1922, the police department of a large city has been constrained by law to allocate an equal number of police officers to each of the three tours of duty (midnight to 8:00 A.m., 8:00 A.M. to 4:00 P.m., and 4:00 P.M. to midnight). In recent years this constraint has been particularly troublesome, since near-saturation loads occur during predictable periods, but to relieve the congestion, additional officers would have to be added to the force around the clock. This is prohibited by budgetary considerations.

Examining this situation, the in-house planning and research group sees an opportunity to use simulation and analytical models in a very important way. Instead of accepting the existing statute as a "given" constraint, the group plans to examine how the patrol force would function if the law were modified to allow tours with nonequal numbers of operating personnel. The group is convinced that the current total number of officers available is sufficient to handle the needs of the city if the tours could be restructured (perhaps even allowing overlapping tours) to reflect the widely varying call-for-service rates and the needs for preventive patrol.

The group initially plans to use queueing models to get a rough idea of the number of personnel required by place and by time of day to achieve a "reasonable level of service." Then response and patrol models will be used to structure thinking about sector design, workloads, preventive patrol coverage, and so on. Finally, several detailed simulation tests will be performed to determine the extent of improvement obtained by reallocating the officers. if the results are sufficiently promising, the group plans to make the findings of the study publicly available. Eventually, it is hoped that this may cause a revision in the current law.

Working as the study group, how do you proceed?

Example 6: Redesigning a City's Ambulance Services

Currently, a city's emergency ambulance needs are handled by several private companies. These companies have been facing a deteriorating financial situation, with labor and maintenance costs increasing and a growing number of indigents unable to pay the cost of ambulance service. The companies cannot afford the expense of highly trained drivers and attendants; but a recently passed state law requires that all drivers have substantial paramedical training by January I of next year. Given this situation, it is highly probable 'hat the private companies will go out of business and that some other means of providing ambulance service will have to be provided.

The mayor's office has requested that a study group examine and evaluate alternative proposals for providing ambulance service:
a. Incorporate ambulance service into police department operations.
b. Have a separate city-sponsored ambulance fleet.
c. Subsidize current companies or a merged version of those companies.

As the appointed study group, structure and analyze this problem, paying particular attention to operational, economic, and service-related issues.