ESSENTIAL FEATURES OF QUEUING SYSTEMS PENTING FEATURES DARI SISTEM ANTRIAN
Figure 11.2 depicts the essential features of queuing systems. These are: 1) calling population, 2) arrival process, 3) queue configuration, 4) queue discipline, and 5) service process. Gambar 11.2 menggambarkan fitur penting dari sistem antrian. Ini adalah: 1) panggilan penduduk, 2) proses kedatangan, 3) antrian konfigurasi, 4) disiplin antrian, dan 5) proses pelayanan.
Services obtain customers from a calling population. The rate at which they arrive is determined by the arrival process. It servers are idle, then the customer is immediately attended; otherwise, the customer is diverted to a queue, which can have various configurations. At this point, some customers may balk when confronted with a long or slow-moving waiting line and seek service elsewhere. Other customers, after joining the queue, may consider the delay to be intolerable, and so they renege, which means that they leave the line before service is rendered. When a server does become available, a customer then is selected from the queue, and service begins. The policy governing the selection is known as the queue discipline. The service facility may consist of no servers (i.e., self-service), one or more servers, or complex arrangements of servers in series or in parallel. After the service has been rendered, the customer departs the facility. At that time, the customer may either rejoin the calling population for future return or exit with no intention of returning. Layanan mendapatkan pelanggan dari populasi menelepon. Tingkat di mana mereka tiba ditentukan oleh proses kedatangan. Ini server yang menganggur, maka pelanggan segera hadir, jika tidak, pelanggan dialihkan ke antrian, yang dapat memiliki berbagai konfigurasi. Pada titik ini, beberapa pelanggan akan tidak senang ketika dihadapkan dengan garis tunggu yang panjang atau bergerak lambat dan mencari layanan di tempat lain. Pelanggan lain, setelah bergabung dengan antrian, dapat mempertimbangkan penundaan itu menjadi tak tertahankan, dan sehingga mereka mengingkari, yang berarti bahwa mereka meninggalkan garis sebelum jasa diberikan. Ketika server tidak tersedia, pelanggan kemudian dipilih dari antrian, dan layanan dimulai. Kebijakan yang mengatur pemilihan dikenal sebagai disiplin antrian. Pusat layanan tidak dapat terdiri dari server (yaitu, self-service), satu atau lebih server, atau pengaturan kompleks server di seri atau secara paralel. Setelah jasa telah
diberikan, pelanggan berangkat fasilitas. Pada saat itu, pelanggan juga dapat bergabung kembali dengan populasi menyerukan kembali masa depan atau pintu keluar dengan tidak berniat kembali.
We shall now discuss in more detail each of these five essential features of queuing systems. Sekarang kita akan membahas secara lebih rinci masing-masing lima fitur penting dari sistem antrian.
Calling Population The calling population need not De Homogeneous; it may consist of several sud-populations. For example, arrivals at an outpatient clinic can be divided into walk-in patients, patients with appointments, and emergency patients. Each class of patient will place different demands on services, but more important, the waiting expectations of each will differ significantly. In some queuing systems, the source of calls may be limited to a finite number of people. For example, consider the demands on an office copier by a staff of three secretaries. In this case, the probability of future arrivals depends on the number of persons who currently are in the system seeking service. For instance, the probability of a future arrival becomes zero once the third secretary joins the copier queue. Unless the population is quite small, however, an assumption of independent arrivals or infinite population usually suffices. Figure 11.3 shows a classification of the calling population. Memanggil Penduduk
Populasi tidak perlu memanggil De homogen, melainkan dapat terdiri dari beberapa tiba-populasi. Misalnya, kedatangan di klinik rawat jalan dapat dibagi menjadi walk-in pasien, pasien dengan janji, dan pasien darurat. Setiap kelas pasien akan menempatkan tuntutan yang berbeda pada layanan, tetapi yang lebih penting, harapan menunggu dari masing-masing akan berbeda secara signifikan.
Dalam beberapa sistem antrian, sumber panggilan mungkin terbatas pada jumlah terbatas orang. Sebagai contoh, perhatikan tuntutan pada mesin fotokopi oleh staf dari tiga sekretaris. Dalam hal ini, probabilitas kedatangan masa depan tergantung pada jumlah orang yang saat ini dalam sistem mencari layanan. Misalnya, probabilitas kedatangan masa depan menjadi nol setelah sekretaris ketiga bergabung dengan antrian mesin fotokopi. Kecuali populasi yang cukup kecil, bagaimanapun, asumsi kedatangan independen atau populasi tak terbatas biasanya sudah cukup. Gambar 11.3 menunjukkan klasifikasi dari populasi menelepon.
Arrival Process Any analysis of a service system must begin with a complete understanding of the temporal and spatial distribution of the demand for that service. Typically, data are collected by recording the actual times of arrivals. These data then are used to calculate interarrival times. Many empirical studies indicate that the distribution of interarrival times will be exponential, and the shape of the curve in Figure 11.4 is typical of the exponential distribution. Note the high frequency at the origin and the long tail that tapers off to the right. The exponential distribution also can be recognized by noting that both the mean and the standard deviation are theoretically equal Kedatangan Proses Setiap analisis dari sistem pelayanan harus dimulai dengan pemahaman yang lengkap dari duniawi dan spasial distribusi permintaan untuk layanan tersebut. Biasanya, data dikumpulkan dengan merekam kali sebenarnya dari pendatang. Data ini kemudian digunakan untuk menghitung waktu antar kedatangan. Banyak studi empiris menunjukkan bahwa distribusi antar kedatangan kali akan eksponensial, dan bentuk kurva pada Gambar 11.4 adalah khas dari distribusi eksponensial. Perhatikan frekuensi tinggi pada asal dan ekor panjang yang berangsur-angsur berkurang ke kanan. Distribusi eksponensial juga dapat diakui dengan mencatat bahwa baik mean dan deviasi standar secara teoritis sama
Queue Configuration Queue configuration refers to the number of queues, their locations, their spatial requirements, and their effects on customer behavior. Figure 11.10 illustrates three alternative waiting configurations for a service, such as a bank, a post office, or an airline counter, where multiple servers are available. Konfigurasi Antrian Konfigurasi Antrian mengacu pada jumlah antrian, lokasi mereka, persyaratan spasial mereka, dan pengaruhnya terhadap perilaku pelanggan. Gambar 11.10 mengilustrasikan tiga konfigurasi menunggu alternatif untuk layanan, seperti bank, kantor pos, atau counter maskapai penerbangan, di mana beberapa server yang tersedia.
For the multiple-queue alternative shown in Figure ll.l0a, the arriving customer must decide which queue to join. The decision need not be irrevocable, however, because one may switch to the end of another line. This line-
switching activity is called jockeying. In any event, watching the line next to you moving faster than your own is a source of aggravation, but the multiplequeue configuration does have the following advantages: 1. The service provided can be differentiated. The use of express lanes in supermarkets is an example. Shoppers with small demands on service can be isolated and processed quickly, thereby avoiding long waits for little service. 2. Division of labor is possible. For example, drive-in banks assign the more experienced teller to the commercial lane. 3. The customer has the option of selecting a particular server of preference. 4. Balking behavior may be deterred. When arriving customers see a long, single queue snaked in front of a service, they often interpret this as evidence of a long wait and decide not to join that line. Untuk alternatif ganda antrian yang ditunjukkan pada Gambar ll.l0a, para cus tiba ¬ Kastamer harus memutuskan yang antrian untuk bergabung. Keputusan tidak perlu ditarik kembali, namun, karena orang dapat beralih ke akhir baris lain. Kegiatan baris-switching disebut berebut. Dalam hal apapun, menonton garis sebelah Anda bergerak lebih cepat dari Anda sendiri adalah sumber kejengkelan, tetapi konfigurasi multi-antrian memang memiliki keuntungan sebagai berikut:
Layanan yang disediakan dapat dibedakan. Penggunaan jalur ekspres di supermarket adalah contoh. Pembeli dengan tuntutan kecil pada layanan dapat diisolasi dan diproses dengan cepat, sehingga menghindari menunggu lama untuk layanan kecil.
Pembagian kerja adalah mungkin. Sebagai contoh, drive-in bank menetapkan teller lebih berpengalaman untuk jalur komersial.
Pelanggan memiliki pilihan untuk memilih server tertentu preferensi.
Balking perilaku mungkin tergoyahkan. Ketika pelanggan tiba melihat antrian panjang tunggal berliku-liku di depan layanan, mereka sering menafsirkan ini sebagai bukti menunggu lama dan memutuskan untuk tidak bergabung garis itu.
Whenever a server becomes available, the first person in line moves over to the service counter. This is a popular arrangement in bank lobbies, post offices, and amusement parks. Its advantages are: 1. The arrangement guarantees fairness by ensuring that a first-come, first- served rule (FCFS) applies to all arrivals. 2. There is a single queue; thus, no anxiety is associated with waiting to see if one selected the fastest line.
3. With only one entrance at the rear of the queue, the problem of cuttingin is resolved and reneging made difficult. 4. Privacy is enhanced, because the transaction is conducted with no one stand ing immediately behind the person being served. 5. This arrangement is more efficient in terms of reducing the average time that customers spend waiting in line. Figure 11.10c illustrates a variation on the single queue in which the arriving customer takes a number to indicate his or her place in line. When using such numbers to indicate positions in a queue, there is no need for a formal line. Customers are free to wander about, strike up a conversation, relax in a chair, or pursue some other diversion. Unfortunately, as noted earlier, customers must remain alert to hear their numbers being called or risk missing their turns for service. Bakeries make subtle use of the "take-anumber" system to increase impulse sales. Customers who are given the chance to browse among the tantalizing pastries often find that they purchase more than just the loaf of fresh bread for which they came. If the waiting area is inadequate to accommodate all customers desiring service, then they are turned away. This condition is referred to as a finite queue.Restaurants with limited parking may experience this problem to a certain extent. A public parking garage is a classic example, because once the last stall is taken future arrivals are rejected with the word FULL until a car is retrieved. Finally, concealment of the waiting line itself may deter customers from balking. Amusement parks often process waiting customers by stages. The first stage is a line outside the concession entrance, the second is the wait in an inside vestibule area, and the final stage is the wait for an empty vehicle to convey a party through the attraction. Figure 11.11 shows a classification of queue configurations. Queue Discipline The queue discipline is a policy established by management to select the next customer from the queue for service. The most popular service discipline is the first-come, first-served (FCFS) rule. This represents an egalitarian approach to serving waiting customers, because all customers are treated alike. The rule is considered to be static, because no information other than position in line is used to identify the next customer for service.
Dynamic queue disciplines are based on some attribute of the customer or status of the waiting line. For example, computer installations typically give first priority to waiting jobs with very short processing times. This shortestprocessing-time (SPT) rule has the important feature of minimizing the average time that a customer spends in the system.7 This rule is seldom used in its pure form, however, because jobs with long operation times would continually be set aside for more recent arrivals with shorter times. By selecting next the job with the shortest service time, excessive delays result for jobs with long service times. Typically, arrivals are placed in priority classes on the basis of some attribute, and the FCFS rule is used within each class. An example is the express checkout counter at supermarkets, where orders of ten or fewer items are processed. This allows large stores to segment their customers and, thereby, compete with the neighborhood convenience stores that provide prompt service. In a medical setting, the procedure known as triage is used to give priority to those who would benefit most from immediate treatment. The most responsive queue discipline is the preemptive priority rule. Under this rule, the service currently in process for a person is interrupted to serve a newly arrived customer with higher priority. This rule usually is reserved for emergency services, such as fire or ambulance service. An ambulance that is on the way to a hospital to pick up a patient for routine transfer will interrupt this mission to respond to a suspected-cardiac-arrest call. The queue discipline can have an important effect on the likelihood that a waiting customer will renege. For this reason, information on the expected waiting time might be made available to the arriving customer, and updated periodically for each waiting customer. This information usually is available to computercenter users who are interested in the status of their jobs waiting in queue to be processed. Some fast-food chains (e.g., Wendy's) take a more direct approach to avoid customer reneging. When long lines begin to form, a service person begins to take orders while customers are waiting in line. Taking this idea further is the concept of round-robin service as used by time-shared computer systems. In
these systems, a customer is given partial service, and then the server moves on to the next waiting customer. Thus, customers alternate between waiting and being served. Figure 11.12 shows a classification of queue disciplines. Service Process The distribution of service times, arrangement of servers, management policies, and server behavior all contribute to service performance. Figure 11.13 contains histograms of several service time distributions in an outpatient clinic, and as the figure shows, the distribution of service times may be of any form. Conceivably, the service time could be a constant, such as the time to process a car through an automated car wash; however, when the service is brief and simple to perform (e.g., preparing orders at a fast-food restaurant, collecting tolls at a bridge, or checking out items at a supermarket), the distribution of service times frequently is exponential (see Figure 11.4). The histogram for second-service times, Figure 11.13c, most closely approximates an exponential distribution. The secondservice times represent those brief encounters in which, for example, the physician prescribes a medication or goes over your test results with you. The distribution of service times is a reflection of the variations in customer needs and server performances. Table 11.1 illustrates the variety of service facility arrangements that are possible. With servers in parallel, management gains flexibility in meeting the variations in demand for service, Management can vary the service capacity effectively by opening and closing service lines to meet changes in demand. At a bank, additional teller windows are opened when the length of queues becomes excessive. Cross-training employees also adds to this flexibility. For example, at supermarkets, stackers often are used as cashiers when lines become long at the check-out counters. A final advantage of parallel servers is that they provide redundancy in case of equipment failures. The behavior of service personnel toward customers is critical to the success of the organization. Under the pressure of long waiting lines, a server may speed up and spend less time with each customer; unfortunately, a gracious and leisurely manner then becomes curt and impersonal. Sustained pressure to hurry may increase the rate of customer processing, but it also sacrifices quality. This behavior on the part of a
pressured server also can have a detrimental effect on other servers in the system. For example, a busy emergency telephone operator may dispatch yet another patrol car before properly screening the call for its critical nature; in this situation, the operator should have spent more time than usual to ensure that the limited resources of patrol cars were being dispatched to the most critical cases. Figure 11.14 suggests a classification of service processes. SUMMARY An understanding of the queuing phenomenon is necessary before creative approaches to the management of service systems can be considered. An appreciation of the behavioral implications of keeping customers waiting reveals that the perception of waiting often is more important than the actual delay. Waiting also has economic implications for both the service firm and its customers. A schematic queuing model identified the essential features of queuing systems: calling population, arrival process, queue configuration, queue discipline, and service process. An understanding of each feature provides insights and identifies management options for improving customer service. In Chapter 17, "Queuing Models and Capacity Planning," we will explore applications of several analytical queuing models that are useful for predicting customer waiting times. These models will suggest further insights that will be helpful in capacity planning and scheduling decisions. KEY TERMS AND DEFINITIONS
