25-28 July 2005, Vla Real, Portugal Modellng a Queung System for a Vrtual Agrcultural Call Center İnc Şentarlı, a, Arf Orçun Sakarya b a, Çankaya Unversty, Department of Management,06550, Balgat, Ankara, Turkey, senta@cankaya.edu.tr b Çankaya Unversty, Department of Management, Ankara, Turkey, sakarya@cankaya.edu.tr Abstract Ths study nvestgates varous queung models that may be mplemented n a vrtual agrcultural call center. The purpose of the call center we consdered s to ease the extenson process whle provdng farmers wth requested nformaton n an nteractve way. The frequency of the questons and the type of actual calls have been taken nto consderaton to formulate a queung system model for ths vrtual call center. A computer code has been developed to predct the random varables and number of servers needed durng the communcaton process. Results, dscussons and further suggestons nvolvng the queung process n the vrtual agrcultural call centers also are presented. Key words: Call Center, Extenson, Server, Queung Models. 1 Introducton To ncrease farmers performance, one of the most mportant factors s to enhance hs techncal knowledge by agrcultural extenson and hs partcpaton n the decson process. Communcaton technologes can be used as a facltatng tool for nformaton acquston and sharng n the sector. Moreover, especally to contrbute to the polcy formulaton, t s essental for the farmers and other actors of the agrcultural sector to access government representatves n a practcal manner. An agrcultural call center s a place where farmers and other telephone calls are handled by an organzaton for agrcultural purposes (Sakarya and Şentarlı, 2003. In ths call center, whch manly serves the farmers and agrcultural organzatons, dfferent types of questons can be asked. These questons can be related to economcs such as government supports; commerce such as marketng and export nformaton and growng nformaton. The staff reples the ncomng calls and records data retreved from the callers n a database fle. These data can also be updated whenever t s necessary and can be used for polcy decsons. However, the man goal of such a call center s to ease the extenson process and solve dfferent types of problems whle ncreasng farmer s level of knowledge. To acqure the msson of the call center, dfferent types of technology can be used. To track farmer data from hs personal fle that contans nformaton such as address, locaton, ID, and a detaled land nformaton.e. crop harvested, yeld and rrgaton; a Computer Telephony Integraton (CTI mplementaton can be used. Ths technology allows the agent to track the related nformaton smultaneously whle he s on the phone and even to update t wth new questons. Wthn the process, the farmer wll automatcally be recognzed by the system wth the help of hs already recorded phone number. Customers may access to the call center toll-free. Calls are dstrbuted to the agents evenly wth a system called Automatc Call Dstrbutor (ACD. After recognzng the farmer; dfferent types of problems can be solved by the agents who are generally experts n dfferent areas of agrculture. In ths step, nature of the questons answered and the problems solved dentfes the scope of the servce provded by the center and the workload of the agents. Another factor that affects agent workload s the number of ncomng calls, that s the demand for the call center. Ths demand can be fluctuated by the number of callers and the degree of satsfacton from the servce. In both cases, there s a possblty that at least two persons or more can call the center smultaneously. When there are multple smultaneous calls, t s 450
25-28 July 2005, Vla Real, Portugal possble that there s a queue dependng on the frequency of the call arrvals and provded servce tme. Ths means that there wll also be watng customers to be served n the system. Basc elements of a queung system consst of the followng components: customer populaton, customer arrvals, watng lne, servce facltes and served customers. Watng lnes form because people or thngs arrve at the servce faclty or server faster than they can be served. The man reason for the queues s the unequal servce tme and dfferent dstrbuton of random arrvals of customers. The nput source to a queue can be from a lmted or an unlmted populaton. In addton to that, customer behavor can vary n a queue. They can prefer not to wat longer and leave the queue and they are treated as loss customers n the system. Another case s when the queue s too long, arrvng customers may not prefer to jon the queue. All of these behavors are expressed by the queue dscplne such as frst-come-frst-served, lastcome-frst-served, random selecton, prorty or general or server structures such as sngle-channel sngle-phase, sngle-channel, multple phase, multple-channel, sngle-phase, multple-phase. The frst mportant beneft of the queung system s the publc servce provded. All the regstered farmers whose telephone number s recognzed by the system wll be able to call the center to obtan a servce. As the center gves a publc servce, we should also add other potental callers to ask questons or to request help. Ths ends up wth a large volume of an nput source who can call from anywhere n the country n a random manner. Even though the number of callers s dfferent n dfferent regons, no regon n the country has a prorty. Moreover, as a general behavor n the call centers, the queue dscplne works on frst-come-frst-served bass. The system can handle multple calls at the same tme and when the frst farmer reaches the last avalable agent the rest of the callers wll have to wat on the phone lne and form a queue. Nature of the questons and the servce tmes are also mportant factors that affect the performance of the queung system. For example, servce tme for a queston concernng a new state support may be dfferent from the one that nvolves a phytosantary measure. That stuaton also affects the server s performance and the number of free servers, because the servce tmes and the number of questons to be answered are not restrcted. In addton to servce tme factors, we should also consder the fact that the number of the agents cannot be easly augmented because of the budgetary constrants. Optmal desgn of processor sharng queung systems have been studed by Yamazak (1987, De Waal (1993 and Aksn (2003, 2001, 2000. Aksn also has focused on some performance measures of the call center system such as blockng probabltes (2001. In ths study, a vrtual call center wth processors shared by dfferent departments has been studed to understand the varous factors that affect such an agrcultural queung system. 2 Investgatng Queung Models When queung models are nvestgated, t s essental to know some basc termnology and notatons that are commonly used n dfferent types of models (Saaty 1983, Allan 1990, Gross and Harrs, 1998. These notatons wll gve the possblty of understandng dfferent combnatons between queung elements and so the theores. To overvew a queung process, t s mportant to understand the followng dmensons explaned n ths secton. Two basc parameters play an mportant role durng the process. One of these parameters s the mean arrval rate (λ and the other one s mean servce rate (μ. These parameters are used to obtan the expected nterarrval tmes (1/ λ and servce tmes (1/ μ. The dstrbuton of the servce tmes and nterarrval tmes consttute the system patterns. It s also necessary to calculate to the probablty of havng zero customers n the system (P 0 to fnd out the random varables such as number of customers (N and watng tme (W n the queue. The summaton of the customers beng served (N s and the watng customers (N q gves the total number of customers consdered. Nature of servers (S whch may vary accordng to the number of exstng channels dentfy the system chracterstcs. It s also useful to know some elementary relatonshps between these random varables, for example, Lttle s law (Allen, 1990. Evaluaton and usage of these varables can be dfferent n dfferent models dependng on the customer habts, nput source sze and servce polces (sngle/multple servce channels but also the tme perod consdered because the nterarrval and servce-tme dstrbutons wll change. In selectng the best sutable queung model, the queung systems wth dfferent combnatons of patterns and characterstcs that are specfcally used n ths feld are to be nvestgated. In a queung process, arrval and servce patterns are prmarly used and they act as the ntal system dentfers respectvely. The remanng part 451
25-28 July 2005, Vla Real, Portugal of the process s made up by three characterstcs as the number of parallel servce channels; the restrcton on system capacty and the queue dscplne respectvely. In a queung model, the frst two dentfers and the frst characterstc are compulsory to defne queung process. The last two characterstcs are optonally used n defnng the process and they are taken as default characterstcs f they are not stated n the model. The queung process descrbed above s shown by a seres of symbols and slashes such as A/B/X/Y/Z. Some basc types of patterns and characterstcs representng these notatons are summarzed n the table below. Lastly, as already stated, the queue dscplne s mostly FCFS n call centers, that s, the frst caller wll frst be served. Table 1. Queung Notaton A/B/X/Y/Z (Gross and Harrs, 1998 Pattern &Characterstcs Interarrval-tme dstrbuton (A Servce-tme dstrbuton (B Number of parallel servers (X Restrcton on system capacty (Y* Queue Dscplne (Z* *Optonal Explanaton Exponental Determnstc Erlang type k(k=1, 2, Mxture of k exponentals Phase Type General 1, 2,, 1, 2,, Frst come, frst served(fcfs Last come, frst served Random selecton for servce Prorty General Dscplne 3 Descrpton of the model used for the vrtual call center In ths study, M/M/S model has been selected and a computer code has been developed for the computatons requred. For ths model, a call center wth K access channels has been consdered wth a processor sharng servce dscplne. A couplng may occur due to ths common nformaton processor whch results n servce rate changes. In addton, customer losses are also ncluded nto the calculatons and the blockng probabltes have been used to reflect the effect of these losses on the system. In ths call center descrbed, the goal s to determne the optmal number of servers who are servng n dfferent departments. Arrval rate of customers that ndcates the center s workload and servce rate that affects the effcency of the system have been utlzed as nput values for the calculatons. Usng a lnear programmng method, ths problem has been reduced to a canoncal form. The followng equaton whch represents the objectve functon, gves the optmal number of servers provdng maxmum proft for the center. V s the revenue generated from each customer n department, λ refers to total arrval rate for department, BB gves the blockng probablty for department, S denotes the number of servers n each department, C s the server cost. K max [ νλ(1- B (S - C (S s = 1 ] =1,2,,K (1 In ths canoncal form, steady state condtons (Saaty, 1983 and the total number of avalable servers consttute the constrants. The blockng probablty s calculated accordng to the followng formula where, ψ gves the multnomal dstrbuton (Equaton 2. 452
25-28 July 2005, Vla Real, Portugal B ψ ( N ψ ( N = 1 =1,2,,K (2 ψ ( N In equaton 2, n gves the number of customers n the queung system n department and μ s the servce rate provded n department. K N λ ( ( N N... N! 1 1 2 ψ N = + + + =1,2,,K (3 = 1 μ N! Coupled servce rate can be computed by usng Equaton 4 (Aksn, 2001, N μ μ (N = 1+ α (N +... + N K 1 =1,2,,K (4 1 The probablty of havng zero customers n the system where couplng effects exst s calculated accordng to Equaton 5, 1 P 0 = N S 1 S 1 λ + 1 λ S μ N! μ = S! μ Sμ λ 0 =1,2,,K (5 Number of customers n the coupled queung system n each department s computed by the followng formula, λμ N ( λ μ = 2 ( S 1!( Sμ λ s P 0 λ + μ =1,2,,K (6 System utlzaton rato s an mportant factor n assessng the system performance under couplng, therefore t s calculated as, Steady state condton s; λ ρ = =1,2,,K (7 μ S μ S λ =1,2,,K (8 Ths condton should be satsfed n order to obtan the optmal values. Snce the equatons stated above are mplct n S values, the successve substtuton has been used as a convergence method to fnd out the fnal values. 4 Numercal Examples We assume three departments n the vrtual agrcultural call center. The frst department deals wth the economc ssues and answers questons such as supports and payments concernng stockbreedng, premums and so on. The second department gves raser and farmer calendar nformaton and the thrd one reply questons about marketng and foregn trade actvtes. 453
25-28 July 2005, Vla Real, Portugal Usng the code developed for ths study, server allocatons have been computed for dfferent cases (Table 2. For dfferent arrval rate (λ and servce rate (μ values calculated probablty of havng zero customers n the system (P 0,blockng probablty (B, total number of customers n the system (N, coupled servce rate (Coupled μ,utlzaton factor (ρ are gven n addton to the optmum number of servers (S needed n each department. In the calculatons, the call center s assumed to be a publc servce and the revenue generated by the customer (v s taken as zero. Table 2. Server Allocatons of the queung system n a call center wth three departments; a Case 1 Department λ μ P 0 B N Coupled μ ρ S 1 7.8 1.6 0.0701 0.7273 5.5 2.7586 0.5655 5 2 12.6 1.65 0.0262 0.5774 19.6 3.4285 0.4593 8 3 18.0 2.59 0.0107 0.6951 7.16 3.7770 0.6808 7 b Case 2 Department λ μ P 0 B N Coupled μ ρ S 1 10.2 1.6 0.0364 0.9952 19.4 1.1002 1.3244 7 2 16.8 1.65 0.0094 0.0048 10.1 1.3802 1.1065 11 3 24.0 2.59 0.0028 0.9999 33.3 4.0468 0.5930 10 c Case 3 Department λ μ P 0 B N Coupled μ ρ S 1 6.6 1.6 0.1166 0.9183 18.6 2.9629 0.4455 5 2 13.2 1.65 0.0295 0.4115 8.2 3.7183 0.4437 8 3 12.3 2.59 0.0257 0.6700 5.8 2.9431 0.8358 5 When three cases are compared wth each other, maxmum number of servers s needed n Case 2 and least number of servers s computed for Case 3. Even though observed servce rates are the same n all cases, coupled servce rates come out wth dfferent values. Hghest coupled servce rates belong to Case 2. Observed arrval rates are dfferent for three cases and the hghest arrval rates also belong to Case 2. Utlzaton ratos that mply the system performance take the hghest values for Case 1. In these condtons, maxmum total number of customers has been served n Case 2. The total number of servers needed n Case 2 s almost %55 greater than Case 3. 5 Concluson In ths study, a vrtual agrcultural call center wth three departments has been assumed where workloads and servce performances are dfferent n each of them. Varous methods have been nvestgated to understand the call center features and specfc patterns have been selected to characterze the vrtual call center. In the case studes, the effects of dfferent arrval rates on the number of servers and system utlzaton have been examned. As the demand for nformaton ncreases, more servers are needed to mantan the system performance level. There also are admnstratve constrants such as the budget whch affects the recrutment of optmal number of servers. To have the sustanablty of such a center, systems experencng dfferent queung patterns and chracterstcs are suggested to be surveyed. For future research, expermental analyses are recommended to be conducted n call centers to show how close are the computed values to the measured ones. 454
25-28 July 2005, Vla Real, Portugal 6 Nomenclature v = Revenue generated from the customer n channel λ = Customer arrval rate n department BB = Blockng probablty of channel S = Number of servers n department C = Server cost for a sngle tme perod n department μ = Coupled servce rate n channel N = Number of customers served n department ρ= System utlzaton rato n channel α = Couplng coeffcent P 0 = Probablty of havng zero customer n the system 7 References Aksn, O.Z., Harker, P.T. 2003. Capacty szng n the presence of a common shared resource: dmensonng an nbound call center, European Journal of Operatonal Research 147, 464-483. Aksn, O.Z., Harker, P.T. 2001. Modelng a phone center: analyss of a multchannel, multsource processor shared loss system, Management Scence 47(2, 324-336. Aksn, O.Z., Harker, P.T. 2000. Computng performance measures n a mult-resource processor- shared loss system, European Journal of Operatonal Research 123, 61-72. Allen, A.O. (Eds., 1990. Probablty, Statstcs and Queung Theory wth Computer Scence Applcatons. Academc Press Inc., Boston. DeWaal, P. 1993. A constraned optmzaton problem for a processor sharng queue, Naval Research Logstcs 40, 719-773. Gross, D., Harrs, C. (Eds., 1998. Fundamentals of Queung Theory. John Wley and Sons Inc., New York. Saaty, T.L. (Eds., 1983. Elements of Queung Theory wth Applcatons. Dover Publcatons Inc., New York. Sakarya, A.O., Şentarlı, İ. 2003. An IVR/CTI supported call center desgn for agrcultural purposes n Turkey, ITAFE 03 Proceedngs, 280-285. Yamazak, G., Sakasegawa H. 1987. An optmal desgn problem for lmted processor sharng systems, Management Scence 33(8, 1010-1019. 455