Sistema:
Nº de matrículas efectuadas/dia: 100 (mediante apresentação de senha)
Distribuição de senhas: Todas as manhãs, às 8:30
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Horário das matrículas propriamente ditas: Das 9:00 às 12:00 e das 14:00 até terminarem as senhas
distribuídas no dia
The total time spent by students waiting equals the difference between the cumulative arrival and the cumulative departure times. One way to reduce this time is by making the arrival process more closely match the registration process.
To alter the arrival process, a reservation system might be implemented so that students arrive at constant intervals or registration hours might be changed to spread out student arrivals. These are mechanisms for encouraging students to arrive at the best possible times.
If each student is induced to change its arrival time to the time it departs from queue, the queue would disappear. The queue would disappear without changing the times students depart from the system.
In a sense, one can say that predictable queues are caused by students arriving at the wrong times. Why should students arrive any earlier than the time they begin registering? Why not arrive when a registrar employee is available?
Registrars have capacities. Going beyond capacity benefits no one and, perhaps, hurts everyone. Allowing students to arrive at a faster rate than they can be registered delays every student in the queue.
One should keep in mind that altering the arrival process does not come without cost. Reservations pose some inconvenience to students, though the inconvenience is usually preferable to the waits that would otherwise result.
Reservation and Appointment Systems
Reservations and appointments are two names for the same idea – a system whereby the student contacts the registrar in advance to schedule a time to perform the registration. Reservations and appointments are common. They are especially common for queuing systems with long service times (10 or more minutes).
Reservations should encourage students to arrive at a constant rate matching the rate of registration. Students arrive at a constant rate because they are scheduled to arrive at a constant rate. Thus, the contribution of reservations is the elimination of predictable queues. To a lesser extent, reservations systems can also help eliminate stochastic queues by reducing the variation in student interarrival times. But this depends on student punctuality. If students do not arrive precisely on time, particularly if the spacing between appointments is small, then the arrival process will resemble a Poisson process and the reservation system will not eliminate stochastic queues.
There is an important danger in reservations: They tend to mask queuing problems rather than eliminate them. The presence of a student waiting in the hall provides a constant reminder to the registrar that queues are a problem. A student waiting at home for an appointment does not. But whether in a hall or at home, the student is still part of a queue.
Worthington’s 1987 article on the United Kingdom’s health service is informative. He states: “Waiting lists have been an unsatisfactory feature of the National Health Service (NHS) since its inception in 1948. In part, they are a necessary evil in that they provide a pool of students to ensure that expensive health-service resources do not lie idle for the want of suitable students. However, waiting lists are usually much bigger than is necessary for this purpose.” From this statement, it is apparent that the MHS reservation system has led to a perpetual queue – a queue in which all students wait for appointments. Reservations reduced the cost of providing the service (by reducing the number of servers) but do not improve the quality of the service.
This is not to say that reservations are a bad idea. On the contrary, they can be very effective at eliminating queues. The message is that reservations should not be used with the purpose of achieving 100 percent registrar utilization. Further, the appointment queue should be constantly monitored to ensure that students do not have to wait excessive lengths of time for their appointments.
Two types of reservation systems have been studied the most. In one of them the system commonly operates with a single server queue, even when several clerks work at the same time. Registrars operate more or less on a continuous basis for periods up to seven hours, the length of a registration day. For the registrar, the issues are the spacing between appointment times and the number of students scheduled for each appointment time.
Soriano classifies appointment systems into four types: pure block appointment systems, individual appointment systems, mixed block-individual appointment systems, and other systems
A pure block system assigns a common appointment time at the beginning of the day for all the students scheduled to be registered at on any given day. An individual appointment system is one in which each student is assigned a different appointment time, and these times are equally spaced through the registration hours. A mixed block-appointment system arranges for an initial group of students to arrive at opening time with others scheduled to arrive at equally spaced intervals.
From the registrar’s perspective, the advantage of the pure block system is that clerks are kept busy from the beginning of the registration day until the last student is registered. But from the student’s perspective, the pure block system is a disaster. It forces students to arrive much earlier than they could possibly be served. The individual appointment system is more sensible, considering that the registration operates as a single server queue. In essence, the registrar’s schedule for the day is determined in advance by the appointment schedule. Students are scheduled to arrive at the same rate that they are served and, one hopes, neither waiting time nor the idle time is large. The motivation for the mixed block-individual system is that queueing systems do not instantly enter steady state at the beginning of the day. It takes time for the system to “warm up.” The warm up phase might be eliminated by scheduling extra appointments at the start of a registration day. This in turn can eliminate registrar idle time.
Bailey (1952), Jackson (1964) and White and Pike (1964) studied the impacts of changing the appointment interval, the time separation between appointments. In all of these studies, the major concern was balancing a trade-off between registrar idle time and student waiting time. For example, Jackson collected data on service times in the United Kingdom, observing a mean of 4.55 minutes. By way of simulation, he then applied the data to varying appointment intervals, assuming that students arrive on time over a registration session lasting two hours (registration continues until the last student is registered).
Shortening the interval between appointments reduces registrar idle time and increases student waiting time. This relationship is highly nonlinear: Small changes in the appointment interval have a large impact on waiting time when the intervals are small. Jackson writes: “It is worth noting that the reason the students’ average waiting time does not become infinite when the appointment interval is less than the average registration time is that it is not an infinite queueing system.” Student waiting time depends on the length of the registration procedure. A short appointment interval may be satisfactory when the registration procedure is relatively short. A short procedure provides an earlier opportunity for the registrar to “catch up” with arrivals. It is worth noting that the system may never approach steady state. Therefore, the steady state models are not applicable.
At least as important as the waiting time per student is the total student waiting time. For an appointment interval of six minutes, a wait per student of two minutes translates into a total student waiting time of 40 minutes over two hours, a value that exceeds the registrar idle time. An appointment interval of five minutes creates more than ten times as much waiting time as registrar idle time. This suggests that the appointment interval should be somewhat longer than the mean service time. Nevertheless, a two to five minute wait per student is probably tolerable, given that students are unlikely to arrive at their precise appointment times anyway.
Welch’s 1964 study of the mixed block-individual system provided results on the impact of scheduling multiple students at the start of a registration day. Welch assumed that both the appointment interval and that mean service time are five minutes, and that 25 students are served. As might be expected, the more students that are scheduled at the start, the longer is the student waiting time and the shorter is the registrar idle time. Both Welch and White and Pike suggest scheduling two students at the start of the registration to achieve a balance between registrar idle time and student waiting time. However, this conclusion is premised on equating registrar idle time to waiting time per student. A fairer comparison would be to total student waiting time. In Welch’s study, scheduling two students at the registration’s start created 40 times as much waiting time as registrar idle time!
It is unfortunate that student waiting time far exceeds registrar idle time in most registrations. The evidence for this is obvious - just compare the average number of waiting students to the average number of idle clerks. Whereas somewhat more waiting time than idle time is justified (due to value of a registrar’s time and the willingness of students to endure short waits), typical waits far exceed reason. (I have been told by one expert in this field that some registrars do not believe that they should ever have to wait for students).
Setting Practical Appointment Times
One of the practical considerations in setting up a reservation system is that appointment times should be rounded to useful numbers - for example, to five, ten, or fifteen minute increments. Little is gained by setting an appointment at 8:07, say, because the student will round the time to 8:05 or 8:10 anyway.
A second practical consideration is that the registration time can be predicted in advance. The reservationist should assess the nature of the student service and assign him or her an appropriate appointment interval.
A final practical issue is that registration times are influenced by the size of the appointment intervals. That is, clerks tend to work faster when students are scheduled to arrive at a faster rate. Some queue operators reduce the appointment interval with the explicit intention of forcing greater output from the clerks. This is a dangerous practice, for it might be detrimental to service quality. On the other hand, there is also a danger in setting the appointment interval too long: It encourages the clerk to take more time than necessary. This is an important dilemma, but is also a dilemma that is best addressed with techniques that fall outside the traditional realm of queuing (for example the methods of industrial psychology and organizational behavior). The thing to recognize is that service times are not necessarily hard-and-fast numbers, and that they are influenced by the reservation system.
“No-shows” (and to a lesser extent, cancellations) is an important issue for all types of queues. In fact, no-shows is probably the biggest weakness of reservation systems. If the student does not show up, the registrar might be left with a block of time that cannot be used productively. Effort should be taken to ensure that students do show up, possibly charging no-shows a fee. Beyond this, the best way to ensure that students show up is to guarantee prompt service. Why should the student be obliged to arrive on time if the registrar is unable to the same? If no-shows are a problem, perhaps the solution is not to overbook students. The solution may be to reduce student bookings and guarantee prompt service for students.
A related issue is student punctuality. Again, the best way to ensure punctuality is to guarantee that the registrar is punctual. If the registrar is habitually late, students will have little motivation to show up on time. But some registrars take the opposite tack, and actually keep “double books” for their reservations: One time is given to the student and a later time is used internally. This is the wrong attitude, one obviously motivated by a desire to eliminate all registrar idle time at the expense of long student waits.
Registrars must also contend with “wall-in” demand, students who arrive without an appointment. Many registrars view walk-ins as a problem, mostly because they have not established procedures to deal with them. In fact, walk-ins are attractive because they can fill empty slots in the schedule. Walk-ins are usually more than willing to wait, understanding that students with appointments should receive priority. For the registrar, this means that a high level of service can be maintained for students who went to the effort of making appointments, while still achieving a high registrar utilization.
Texto adaptado de
Hall, Randolph W. (University of California at Berkeley)
Queueing Methods: For Services and Manufacturing
Englewood Cliffs, N. J., Prentice-Hall, 1991
Uma das alterações mais frequentes, mas simples, foi a utilização da designação de «student» em vez de «customer» e de «registrar» em vez de «server». Esta alteração tem um grande perigo. É que ela pode levar a esquecer que, no processo de matrícula, os estudantes são os clientes e a divisão académica a servidora.
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