Akinbola Adetunji Hadi Larijani. School of Engineering and Computing Glasgow Caledonian University Glasgow, G4 0BA, UNITED KINGDOM

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1 Proceedngs of the 2008 Wnter Smulaton Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. ENHANCED BANDWIDTH-DELAY BASED ROUTING ALGORITHM FOR A PACKET-SWITCHED VIRTUAL CALL CENTRE ENVIRONMENT Aknbola Adetunj Had Larjan School of Engneerng and Computng Glasgow Caledonan Unversty Glasgow, G4 0BA, UNITED KINGDOM ABSTRACT Tradtonally call centres were based on crcut-swtched systems. But wth the advancement of communcaton technologes, call centres have shfted to packet-swtched systems. Ths packet-swtched system ads the creaton of vrtual Call Centre Envronments. The current dynamc routng algorthms used for crcut-swtched systems do not fully support packet-swtched vrtual call centre envronments. We addressed ths ssue n ths paper by developng a new call routng algorthm capable of supportng ths type of vrtual envronments. Ths was done by performng a comparson study on our hybrd routng algorthm, Enhanced Bandwdth-Delay Based Routng Algorthm. Our hybrd routng algorthm was compared wth a commonly used call routng algorthm known as Mnmum Expected Delay. We used both analytcal and smulaton methods to acheve our goal of comparson study. Call centre data collected from a real-call centre was utlsed to ad our model development, valdaton and scenaro generaton. The results from ths study concluded that under hgh traffc arrval rates, systems runnng EBDRA outperforms MED by possessng a lower probablty of delay. 1 INTRODUCTION 1.1 Background In ths day and age, most of our daly nteractons wth companes and organsatons revolve around call centers. Call centers act as the frst pont of contact wth customers/clents of companes and organzatons. They have a hstory that dates back to the expanson of the ntal Publc Swtch Telephony Network (PSTN) concept that saw physcally wred telephones change from a pont-topont connecton to central telephone swtches around the late 1800 s. The operators of these swtches were the frst telephony call centre agents who answered and patched calls to ther destnaton. The success of an organzaton s hghly dependent on the agents representng the organzaton. Hgh agent effcency and productvty drectly affect the overall call centre performance. The Enterprse Telephony (ET) represents the core on whch tradtonal telephone call centers are bult on. It s a scaled down verson of the PSTN desgned for busnesses and organzatons. Modern call centers on the other hand adapt new technology and meda to further provde addtonal servces and extend capabltes of ETs. These modern call centers are referred to as contact centers. G. Koole and A. Mandelbaum (Koole and Mandelbaum 2001, Koole and Mandelbaum 2002) and R. Stolletz (2003), hghlghted that call centers can be categorze based on the features they possess. Features such as functonalty, sze, geography, agent characterstcs, ntaton of contact and communcaton channel. A general characterstc of a call centre s whether t handles nbound or outbound call traffc (Gans, Koole and Mandelbaum 2003). Call centers can be dvded nto four dstnct layers, the network, equpment, personnel and report layer. The personnel layer s responsble for 60% to 70% of call centre annual expenses (CM Insght, ContactBabel & Call and Contact Centre Assocaton May, 2004). For ths reason call centre managers are always lookng for more effcent ways to extend ther capacty and performance. 1.2 Motvaton Effcent call routng s a tool that can be adapted to mprove call centre performance especally n the case of Vrtual Call Centers (VCCs). Research nto VCCs are very few and far between, ths doesn t te n wth the developments n ths area. Call centers are already adaptng a vrtual nature to try to reduce cost and at the same tme expand ther customer capacty. Fgure 1 shows a dagram representng a Vrtual Call Centre Envronment (VCCE) /08/$ IEEE 2891

2 based on crcut-swtched technology supported by current call routng algorthms covered n secton three. The future s lkely to see the ntroducton of more call centers deployed n a packet-swtched envronment. VCCEs nvolve multple geographcal locatons wth multple groups of agents wth dfferent sklls used to serve multple classes of customers wth dfferent needs (Whtt 2005). It has been noted by N. Van Djk (2000) that delays and queung problems are most common features n networkng and telecommuncaton envronments. Currently the trend beng observed s hardware manufacturers clamng support for VCCE mplementaton, but how ths can be effectvely and effcently used and whether t can be deployed on a large scale s yet to be seen. Advances n technology and ntegraton of synergstc technologes have resulted n the development of numerous features that have enhanced the growth of call centers (Sharp 2003). Fgure 1: CSVCCE wth current call routng algorthms 1.3 Research Questons The dagram n Fgure 2 hghlghts the fact that no call routng algorthm has been tested to verfy full functonalty under the packet-swtched envronment. Ths lead us to defne a new algorthm n secton four, and conduct a performance analyss on t n secton fve. We were therefore motvated to provde answers to the followng research questons, 1. What are the factors that cause delays and queung problems wthn a Packet-Swtched VCCE (PSVCCE)? 2. What metrcs are used n call centers to determne performance levels? 3. What functonal parameters are used to determne success of routng calls to call centers n the PSVCCE? 4. Whch call routng algorthm can be best used to manage calls on a PSVCCE? Fgure 2: PSVCCE lack call routng support 1.4 Research Paper Objectves Most researchers are focused on knowledge drven research whle other are problem-drven orented (Mandelbaum, Sakov and Zeltyn 2001). Ths paper focuses on fndng a practcal soluton to the problem of mplementng a modern VCCE based on packet-swtch technology. Our objectves are dvded nto three, the frst objectve s to look at commonly used crcut-swtched call algorthms and develop a new model capable of creatng a vald VCCE. Ths model wll act as a test-bed for the wellknown call routng algorthm. The second objectve s to use the best performng call routng algorthm dentfed from our prevous objectve to create a new call routng algorthm for packet-swtched envronments. Thrdly, to use the developed VCCE models to perform a comparson study of between our new packet-swtched algorthm wth the best crcut-swtched algorthm dentfed from our frst objectve. 1.5 Contrbuton There are three technques we consdered n achevng the above-mentoned objectves, analytcal modelng, smulaton modelng and measurement. We draw the benefts of usng both analytcal and smulaton modelng forms of research work to acheve the our objectves. Ths was done by contrastng these two modelng technques together. We also used the measurement of a real lfe call centre to act as nput and valdaton data to both modelng technques. Accordng to N. Gans et al, havng analytcal models n one s arsenal, even lmted n scope, mproves dramatcally one s use of smulaton (Gans, Koole and Mandelbaum 2003). The rest of the paper s organzed as follows; Secton 2 descrbes the varous types of VCC and the relevance of remote agents (teleworkers). In Secton 3, we dscuss MED and EBDRA n more detals hghlghtng ther smlartes and dfferences. In Secton 4, we present our analytcal and smulaton models along wth the performance metrcs and mplemented assumptons. Our results are presented and analyzed n Secton 5 drawng up a performance evaluaton concluson on the results. 2892

3 2 VIRTUAL CALL CENTRES AND TELEWORKERS Presently, there are three ways of mplementng a VCC, a fully Crcut-Swtched VCC (CSVCC), a fully PSVCC and thrdly, a hybrd of the two technologes. A typcal CSVCC composes of the followng devces and connectons; a crcut swtch hardware based PBX used for call dstrbuton, Trunk lnes used for nterconnectng the networked call centers as well as termnatng customer calls. Telephone handsets for ndvdual agents, Computer Telephony Integrator (CTI), Automatc Call Dstrbutor (ACD) and Interactve Voce Response unt (IVR) servers. The ACD of a PSVCC network on the other hand s a soft-swtch-based system that resdes on ether an upgrade PBX or a computer server. Ths soft-swtch-based system has the characterstc of separatng the sgnalng components from the devce controllers. These soft-swtchbased systems communcate between the separated components through the packet swtch network. The current VCCE structure s based on two or more dspersed call centers nterconnected together. It s also possble to ntroduce Vrtual Agents (Teleworkers) to further vrtualse the VCCE. Teleworkng has evolved snce the 1970s nto three man types, home-based Teleworkng, satellte offces and moble workng. A phenomenal take off of Teleworkng was predcted to occur (Banes 2002, Baruch 2000, Bryant 2000), however ths expanson of teleworkng has faled to meet the expectatons of the EU Commsson (Bangemann May 1994). The benefts of adoptng teleworkng accordng to Pérez, Sánchez and de Lus Carncer (2002), Markby (1995), Kurkland and Baley (1999), and Shn, Sheng and Hga (2000) are, Increased human resource productvty and savngs on the need to purchase real estate by companes to house ther employees. The most sgnfcant barrers are access to technology and the teleworkng ntegraton nto the company s organzatonal structure. Teleworkng also ntroduce flexblty for both the teleworkers and company, wth evdence that a teleworker s productvty s hgher than that of non-teleworker. S. Banes 2002 (Banes 2002), hghlghts the fact that teleworkng s slow n uptake, whle one of the barrers dentfed n M.P. Pérez et al. (2002) was the naccessblty of the technologcal know how. Moreover to the best of our knowledge current crcut-swtched call routng algorthms and packet-swtched data routng algorthms are nsuffcent to deal wth VCCEs calls based on packet-swtched data. But our call routng algorthm Enhanced Bandwdth-Delay based Routng Algorthm (EBDRA) s amed at facltatng the growth of teleworkers and VCC capacty wthn the VCCE. We developed ths algorthm by frst dentfyng the routng algorthm that functon best under dfferent condtons on crcut-swtched networks. The next phase n the concept was to dentfy the major functonal parameters that affect the routng of calls wthn the PSVCCE. These two elements would then be combned to form our call routng algorthm. 3 CALL ROUTING ALGORITHMS 3.1 Call Routng Strategy The equpment known as ACD perform the call routng functon n a call centre, ths unt uses a routng process or processes to handle and route ncomng calls to ther respectve destnaton. Good routng algorthms can help call centers reduce the number of calls n the system, whch therefore affects servce levels n a postve way. There are two ways call routng algorthms can be mplemented when delverng the calls from the ACD to ether the agents or call centers wthn the VCCE, these two systems are know as push (pre-delvery) and pull (post-delvery). S.A. Pot (2006) descrbes the push system as when arrvng calls are assgned to an avalable agent that s chosen by the ACD, whle the pull system notfes agents about a call n the queue, the call s servced by the agent who reacts the fastest. There are varous types of call routng types mostly provded by the servce provder that utlze the predelvery routng strategy, they range from Area-Code routng, Exchange Routng, Tme-of-Day routng, Day-ofweek routng, Holday Routng, Emergency Routng, All- Trunks-Busy-Routng and Call Allocaton Routng (Gable 1993). Call routng supported by post-delvery make ther routng decsons based on the current state of the VCCE, these call routng types are further dvded nto statc and dynamc routng algorthms. Statc routng algorthms are predetermned rules that are used to specfy where to route the calls, the Bernoull Splttng algorthm (Aran and Levy 1992) and Most Regular Sequence (MRS) (Aran and Levy 1992, Hajek 1985) are good examples of a statc routng algorthm. Dynamc routng algorthms on the other hand, dynamcally alter ther decson makng process to sut the current network state. Examples of dynamc call routng algorthms are Bandwdth-Delay based Routng Algorthm (BDRA) (Wang and Crowcroft 1995), Generalsed Round Robn (GRR) (Aran and Levy 1992); Jon the Smallest Actual Watng tme queue (JSAW) (McDonald and Turner 2000), Jon the Shorter Expected Watng tme queue (JSEW), Jon the Shortest Queue (JSQ) (Ln and Raghavendra 1996, McDonald and Turner 2000, Turner 2000, Whtt 1986), Mnmum Expected Delay (MED) 2893

4 (Kogan, Levy and Mlto 1997), and Shortest Delay Rule (SDR) (Houck 1987, Wnston 1977, Ephremdes, Varaya and Walrand 1980, Weber 1978). Queue centrc call routng algorthms work well for CSVCCE, algorthms such as GRR, JSQ, JSAW, JSEW and MED. Whle some concentrate on just the queue sze (JSQ), other algorthms take other factors nto consderaton when decdng how to handle the call, factors such as number of agents and average servce rate. These added factors help mprove the performance of routng algorthms; therefore algorthms such as GRR, MED and JSAW have an added advantage over the lkes of the JSQ algorthm. The prncple of multple nstances of a call on all call centers queues wthn the VCCE as supported by JSAW s good, however hghly dependent on Intellgent networks (IN). Ths prncple forgoes the servce rate nformaton of each call centre wthn the VCCE by duplcatng a sngle call arrval across all the call centers. Ths works well for small to medum szed VCCEs, however when the network sze ncreases further, more demand would be put onto the IN nfrastructure to try and mantan ths multple call nstance. Therefore resources requred for routng the calls are dverted n tryng to mantan the queue of calls watng to be answered. For ths reason, we focused on GRR and MED, whch utlzes the servce rate and number of calls queued at each call centre of the VCCE to generate an expected delay value to make route decsons. We carred out performance evaluatons for these two algorthms along wth another routng algorthm wth the results and dscussons presented n (Adetunj et al. 2007). 3.2 MED Routng Algorthm The MED routng algorthm operates by assgnng the next ncomng call to the queue whose current allocaton does not exceed the target allocaton and also exhbts the least delay wthn the VCCE. Ths routng algorthm s represented by the equaton shown n (1), the target allocaton refers to the maxmum tme a call s expected to wat n the queue before beng served. r n+1 = mn{;k n (t) np (t)} (1) r n +1 represents the current routng process, s the queue number, k n (t) represents the expected delay of all calls n queue up to and ncludng the nth call arrval, and p s the target allocaton of queue at nstance n. k n s the dervatve of the expected delay equaton shown n (2), and represents the mnmum k from k n < k +1 n <... < k z n. k n (t) = n (t) S +1 S μ (2) n (t) s the number of calls n queue at tme t, S equals the number of agents assgned to queue, whle μ s the exponental servce mean at queue. When a call arrves at a call centre under the nfluence of the MED routng algorthm, the expected delay of the calls wthn the local call centre queue s checked. If t s greater than the target allocaton, ths expected delay s then used to determne the call centre wth the least expected delay wthn the VCCE. Once ths has been ascertaned, the call s routed to the resultng call centre. The MED algorthm has been shown to functon well n a crcut-swtched VCCE (Kogan, Levy and Mlto 1997; Adetunj et al. 2007), however there has not been any paper that addresses call routng wthn packet-swtched VCCEs. We therefore propose n ths paper the EBDRA routng algorthm desgned to take bandwdth nto consderaton when routng calls. The next secton covers the functonaltes of EBDRA. 3.3 EBDRA Routng Algorthm In the CSVCCE, the trunk lne avalablty acts as one of the functonal parameters that determne f a call wll be successfully routed to other call centers wthn the VCCE. However ths doesn t apply to PSVCCEs, a more applcable functonal parameter that determnes the success of routng calls to call centers n the PSVCCE s bandwdth. Bandwdth plays an mportant role as the number of concurrent voce channels depends on the amount of avalable bandwdth. Ths parameter s however not the only functonal parameter used n determnng success of call completon, other parameters that are closely related to bandwdth are, packet loss, Qualty of Servce, codec sze and delay. In order to create a call routng algorthm that functons well wthn a PSVCCE, the benefcal propertes of MED routng algorthm (calls are routed to queues of call centers wth the least delay) s taken and combned wth the consderaton of bandwdth contenton and loss probablty, smlarly to Z. Wang and J. Crowcroft s BDRA (1995). A path (call centre) wth a large resultng value from the EBDRA equaton s lkely to be a better choce n terms of bandwdth, delay and loss probablty. Ths routng algorthm s represented by the equaton shown n (3). Durng the routng process, an update of the current avalable bandwdth s checked to ascertan f t can support a sesson between the agent and the caller. r n+1 = max{;b n (t) np (t)} (3) b n b n n (3), represents the maxmum value from > b n +1 >... > b n z, whch s calculated wth the bandwdth 2894

5 expected delay formula (a combnaton between bandwdth delay and MED) shown n (4). b n (t) = C n k n (t)p B (4) The loss probablty P B n (4) s derved from (5), whch ncludes the blockng probablty and arrval rate λ, whle k n represents the expected delay calculaton (2). P B = λ λ ' λ C n n (4) represents the current avalable bandwdth at queue durng the nth routng process. Calls are therefore routed to the call centre dsplayng the hghest EBDRA value upon completon of the routng process. 4 MODEL DEVELOPMENT The two general models tradtonally used to setup and manage call centers are Erlang B and Erlang C. A Dansh mathematcan called A.K. Erlang n 1917 whle he was wth the Copenhagen Telephone Company developed the Erlang C formula (Cleveland and Mayben 1997, Koole 2002), ths formula s represented by the queung model n equaton (6). (5) M / M /n (6) Our model can be specfed based on the taxonomy for nput models used by L.M. Leems (2004). We therefore base our models around Markov chans, whch s a dscrete-state Markov process. The system represented wth a Markov process moves from one state to another, ths s known as transton and represents occurrences of arrval and servce completon. 4.1 Analytcal Model When representng dfferent call centers, there are dfferent types of analytcal queung models that can be used to represent ther behavor. However, most call centre model representatons use Markov processes. Queung theory s an analytcal technque that s used to analyze systems performance; a Markov process on the other hand represents events, whch are ndependent of past occurrences but dependent on only the present MED Lookng at the complementary CDF delay of MED we developed an analytcal model, ths was done as an expanson to what was already covered by Y. Kogan et al (Kogan, Levy and Mlto 1997). The complementary CDF delay of MED s gven as, F MED(x) =1 F MED (x) (7) Where, F MED Sμx ( x) = e g( x) (8) Therefore, F MED(x) = e Sμx n S j= EBDRA Sμx j! j n= S π MED (n) The EBDRA queung system s represented as a M/M/S/C Markovan mult-server system, wth S representng the number of servers and C representng the space avalable on the trunk/bandwdth concurrency. The bandwdth concurrency represents the total number of calls that can concurrently exst on the lnk wthout congeston occurrng. The blockng probablty s calculated based on the M/M/S/S Erlang s Loss queung system, where there are no watng queues, here arrvng callers that fnd all servers busy are dropped wthout enterng nto the system. Therefore the probablty of fndng all trunks busy or bandwdth fully utlzed s based on the assumpton that S=C and s calculated as, P b = C (Ca) C j= 0 C! (Ca) j j! (9) (10) Ths formula represents the EBDRA functonalty, thereby by combnng both equatons (9) and (10), the delay dstrbuton of EBDRA can be deduced by the resultng equaton n (11). F MED(x) = C (Ca) C j= 0 C! (Ca) j j! e Sμx n S j= 0 Sμx j! j n= S π MED (n) (11) 2895

6 The analytcal models of both the complementary cumulatve dstrbuton frequency of delay for EBDRA and MED were carred out usng MATLAB. The two mathematcal equatons, equaton (9) for MED and equaton (11) for EBDRA were used under MATLAB to compare the dfferences n the generated results whch are dscussed n the next secton. 4.2 Smulaton Model The modelng process adopted s centered on the real world and smulaton world relatonshp wth verfcaton and valdaton modelng defned and explaned by R. Sargent (2004). The real world contans problem enttes that lead to the development of system theores and defntons about the characterstcs of the proposed system that are hghly applcable to the smulaton realm. The real world call centre used was that of an anonymous bank n Israel (Guedj, Mandelbaum 2007). Other sources of call centre data were also consdered, however they lacked vtal nformaton such as data collated based on every entry rather than a sample tme. The smulaton model development process starts wth a system defnton by specfyng the characterstcs of the real world system to be represented n the smulaton world. The real world system data s feed nto the smulaton world to act as a base for valdaton and verfcaton whle the real world system results are used to compare wth the results generated from the smulaton world. Ths technque s used n valdatng and verfyng our smulaton models. We studed the arrval/servce process and nformaton on the collated data to descrbe how calls are processed. Our call centre model s composed of node and process models. The underlyng process models defne the behavor of the node models; each node model contans several process models. Node models specfy the manner of how dfferent functons of the call centre operate and nteract wth each other. The process model on the other hand deals wth the logcal operatons performed on the call, ths secton of our model s represented by C/C Characterstcs and Assumptons Our PSVCCE model s formed from the combnaton of several process and node models. Our model s an extenson from the sngle call centre model developed and valdated n (Adetunj 2007), wth the followng characterstcs and assumptons taken nto consderaton; All models and ther correspondng scenaros were subject to the same traffc traces. All models were also subject to Posson, Exponental and Pareto statstcal dstrbuton, these dstrbuton were used to generate dfferent call arrval rates. The Pareto dstrbuton specfcally smulates bursty perods. Ths allowed us to dentfy how each call routng algorthm manages perods of ntensve traffc arrvals and how these perods affect the system as a whole. Three call centres were nterconnected wth an Internet cloud, the avalable bandwdth for each call centre vared from one scenaro to the next. If there was no avalable bandwdth durng call arrval at the Internet cloud, the calls were queued at the local orgnatng call centre. Three bandwdth sets were used, 8kbps, 200kbps and 400kbps, each representng 1, 25 and 50 concurrent calls because a voce codec of 8kps was used. Sklled-based routng was not consdered n the PSVCCE model and smulaton Call Centre Performance Metrcs Smulaton contrbutes to the development and operatons of call centres, ths was shown n A. Avramds and P. L Ecuyer (Avramds, L'Ecuyer 2005) where decsons based on smulaton modelng had a drect mpact on call centre performance. When conductng experments, t s mportant to know what factors are beng montored and measured. Systems of parameters can be used to perform the requred montorng and measurements needed to provde nterpretatons of the model assessment beng carred out. The nput metrcs are the parameters our models were set to pror to smulaton, after each smulaton run, one or more of these parameters were altered to generate a new scenaro for smulaton. The parameters used were, Call arrval rate Call arrval traces from the real call centre data were used to represent nstances of call arrval n the smulaton model. Also statstcal dstrbutons were also consdered to further test the smulaton models. The dstrbutons consdered were Posson, Exponental and Pareto. Call servce rate Servce rate traces also generated from the real call centre data was used to represent the average servce rate of the smulaton system. Routng Algorthm Two call routng algorthms were used EBDRA and MED. Performance metrcs represent the output metrcs for the system under study; they provde a good way of analyzng the experments under dfferent condtons and scenaros. The type of metrcs used depends hghly on the type and methodology of the experment beng carred out. The followng performance metrcs were used to evaluate the varous models developed and smulated, 2896

7 Call delay - Ths represents the total call delay experenced by callers wthn the call centre or VCCE for the duraton of the call. The call delay startng tme normally starts from the moment the call enters the system on the trunk lnes to when the call has been servced by an agent or IVR and released; ths also ncludes the tme spent n queues. Agent Utlsaton - Ths represents the number of earned hours of each agent over the number of scheduled hours, n others words t s a measure of the degree to whch each agent s used. The hgher the utlsaton means the hgher the frequency and duraton the agent s engaged wth callers. Call Centre Throughput - Throughput n terms of call centers and VCCE s the number of calls processed by the call centre per tme unt. The throughput of a call centre gves an dea of the effectveness of that call centre. Hgher throughput means hgher amount of calls are beng answered wthn a specfc tme unt. Queue lengths - Queue lengths represent the number of calls that are queued at any gven tme of the smulaton s lfe span. A queue s used to hold arrvng calls n the event a CSR or IVR port s unavalable to servce the caller. Calls watng n queues contrbute to the overall delay experenced by the call centre; therefore the performance of the call centre can be montored to some extent wth the use of real tme queue analyss. 5 RESULTS AND ANALYSIS 5.1 Matlab Results Fgure 3a and b represents outcomes of the analyss when the traffc ntensty s at 4.4 but at dfferent tme scales, 500 and 1000 seconds wth 25 calls n the system. From the comparson of both graphs, we deduced that as the tme ncreases from 0 to 1000, the probablty of the occurrence of delay reduces. It s also noted that both EBDRA and MED merged when F [MED/EBDRA] (x) = 550secs at a crossover pont x 0, where F (x 0 ) < 0.1 n Fgure 3b. F(x) represents the outcome on the probablty the watng tme s greater than x. EBDRA n the graphs shows a better performance n mnmzng the probablty of delay for watng tmes less than x. As the number of calls n the system s ncreased to 30 (Fgure 4a and b), the probablty of delay was prolonged n both EBDRA and MED. There s also an ncrease n the cross over pont x 0 for MED to merge wth EBDRA, ths occurs when x 0 = 1000secs where F (x 0 ) < 0.1 n Fgure 4b. (a) (b) Fgure 3: Results of analytcal modellng wth 25 calls n the system (a) for 500secs (b) for 1000secs (a) (b) Fgure 4: Results of analytcal modellng wth 30 calls n the system (a) for 500secs (b) for 1000secs 5.2 OPNET Results The averages of all call centers data wthn the PSVCCE were taken for each bandwdth scenaro and compared wth each other. We outlne our man results below: Queue Length The EBDRA algorthm always showed a reduced queue length when compared to the correspondng MED results under low bandwdth condtons. Ths can be seen n Fgure 5(a). However as the bandwdth avalablty ncreases, both algorthms merge at 400kbps. Fgure 5(a) also shows EBDRA systems possessng lower queue lengths when compared to the systems runnng MED when Posson dstrbutons s used Call Delay The call delays experenced by the PSVCC usng the EBDRA algorthm were lower than the call delay tmes experenced by the PSVCC under the nfluence of the MED algorthm. Also as the bandwdth avalablty 2897

8 ncreases, both algorthms merge at 400kbps (see Fgure 5(b)). Fgure 6b on the other hand represents results from usng a Posson dstrbuton to generate traffc flow. Call delay s also shown to be lower n systems runnng EBDRA over MED. Average Queue Length Average Delay makng a total of 240 agents per PSVCCE. Ths was done to see f the EBDRA algorthm can support a larger call centre wth ncreased amounts of call arrvals and processes. The results that are presented below n Fgure 6 follow the same trend for systems runnng the EBDRA. Showng that the systems runnng the EBDRA call routng algorthm perform better than those runnng on MED Bandwdth (kbps) Bandwdth (kbps) Posson Queue Length: (a) (b) Bandwdth (kbps) Bandwdth (kbps) Average Utlsaton Average Throughput (a) (b) Bandwdth (kbps) (c) Bandwdth (kbps) (d) µ= Bandwdth (kbps) µ= Bandwdth (kpbs) Fgure 5: Shows graphs of real nput data EBDRA and MED smulaton results (a) Average Queue Length (b) Average Delay (c) Average Utlsaton (d) Average Throughput Agent Utlzaton Agent utlzaton n the PSVCC usng EBDRA call routng algorthms were lower when compared to that of MED, however these trend was reversed when the bandwdth avalablty ncreased to 200kbps (see Fgure 5(c)). Although the MED results ended up lower than EBDRA, t stll possessed a hgher utlzaton at bandwdth levels of 400kbps n comparson to EBDRA at the 8kbps level Throughput The man trend notced n ths graphcal representaton of throughput results presented n Fgure 5(d) was, the throughput of the PSVCC runnng EBDRA was hgher than the PSVCC runnng MED. We further tested our models by scalng them up to support 80 agents at each call centre wthn the PSVCCE, (c) Fgure 6: Shows graphs of real nput data EBDRA and MED smulaton results (a) Average Queue Length (b) Average Delay (c) Average Utlsaton (d) Average Throughput 6 CONCLUSION Modern call centers operate under many uncertantes and complextes (Avramds, L'Ecuyer 2005), we therefore tred to tackle ths problem by developng a call routng algorthm that s capable of mprovng the VCC performance. We went about achevng ths goal by developng VCC models usng the OPNET MODELER and analytcal models usng Matlab. Performance comparson was then carred out on our algorthm, EBDRA and one of the most commonly used call routng algorthms, MED. The overall results from the Matlab analyss on the EBDRA and MED models showed that the probablty of delay greater than x for models runnng EBDRA were lower than that for models runnng MED. We also showed (d) 2898

9 that the mergng ponts x 0 of the probablty of occurrence of delay of the two algorthms ncreased as the number of calls n the system ncreased. Ths also causes the mergng ponts between the two algorthms to ncrease, wth the MED system takng longer to merge wth the EBDRA system, as a result EBDRA possesses a performance advantage over MED. From our Opnet results, t can be seen that EBDRA Algorthm performs well durng tmes of low bandwdth avalablty and hgh bandwdth contenton even when statstcal dstrbutons were used to generate call traffc. However n some cases, wth a combnaton of dfferent factors, t was noted that such a performance advantage of EBDRA became nsgnfcant when enough bandwdth became avalable. Current VCC networks are showng trends of vrtualzaton based on agents rather than just call centers, ths type of network creates a more dstrbuted envronment that s solely based on packet swtchng. The EBDRA call routng algorthm can be used to ncrease the effcency and productvty of such a vrtual envronment because the bandwdth avalablty s taken nto consderaton durng the route decson process, thereby accommodatng the varyng effects of bandwdth sze on packet swtched networks. 7 REFERENCES Adetunj, A.O. Dec. 2007, "Call Centre Smulaton Modellng and Analyss", Proceedngs of the IASK E- Actvty and Leadng Technologes, pp Adetunj, A.O., Shahrab, A., Larjan, H. and Mannon, M. Jul. 2007, "Performance Comparson of call routng algorthms over Vrtual Call Centres", The 18th Annual IEEE Internatonal Symposum on Personal, Indoor and Moble Rado Communcatons. Aran, Y. and Levy, Y. 1992, "Algorthms for generalzed round robn routng", Operatons Research Letters,, no. 12, pp Avramds, A.N. and L'Ecuyer, P. 2005, "Modelng and Smulaton of Call centers", Proceedngs of the 2005 Wnter Smulaton Conference, pp Banes, S. 2002, "New technologes and old ways of workng n the home of the self-employed teleworker", New Technology Work and Employment, vol. 17, no. 2, pp Bangemann, M. May, 1994, Recommendatons to the European Councl: Europe and the global nformaton socety, Europe and the global nformaton socety. Baruch, Y. 2000, "Teleworkng: benefts and ptfalls as perceved by professonals and managers", New Technology, Work and Employment, vol. 15, no. 1, pp Bryant, S. 2000, "At home on the electronc fronter: work, gender and the nformaton hghway", New Technology, Work and Employment, vol. 15, no. 1, pp Cleveland, B. and Mayben, J. 1997, Call Center Management on Fast Forward: Succeedng n Today's Dynamc Inbound Envronment, Call Center Press. CM Insght, ContactBabel and Call and Contact Centre Assosaton May, 2004, The UK Contact Centre Industry: A Study., UK Department of Trade and Industry. Ephremdes, A., Varaya, P. and Walrand, J. 1980, "A SIMPLE DYNAMIC ROUTING PROBLEM", Ieee Transactons on Automatc Control, vol. 25, no. 4, pp Gable, R.A. 1993, Inbound Call Centers: Desgn, Implementaton, and Management, 1st edn, Artech House, Massachusetts, USA. Gans, N., Koole, G. and Mandelbaum, A. 2003, "Telephone Call Centres: Tutoral, Revew, and Research Prospects", Manufacturng and Servce Operatons Management, vol. 5, pp Guedj, I. and Mandelbaum, A. 2007,, "Anonymous Bank" Call-Centre Data Documentaton. Avalable: orks.html [2007,. Hajek, B. 1985, "Extremal splttngs of pont processes.", Mathematcal Operaton Research, vol. 10, no. 4, pp Houck, D.J. 1987, "Comparson of Polces for Routng Customers to Parallel Queueng Systems", Operatons Research, vol. 35. Kogan, Y., Levy, Y. and Mlto, R.A. 1997, "Call routng to dstrbuted queues: Is FIFO really better than MED", Telecommuncaton systems, vol. 7, pp Koole, G. 2002, "Call center mathematcs", Draft of a book, vol. 6. Koole, G. and Mandelbaum, A. 2001, Queueng Models of Call Centers: An Introducton. Koole, G. and Mandelbaum, A. 2002, "Queueng models of call centers: An ntroducton", Annals of Operatons Research, vol. 113, no. 1-4, pp Kurkland, N.B. and Baley, D.E. 1999, "The advantages and challenges of workng here, there anywhere, and anytme", Organzatonal Dynamcs, vol. 28, no. 2, pp Leems, L.M. 2004, Buldng credble nput models,. Ln, H. and Raghavendra, C.S. 1996, "An Approxmate Analyss of the Jon the Shortest Queue (JSQ) Polcy", IEEE Transactons on Parallel and Dstrbuted Systems, vol. Vol 7, no. 3. Mandelbaum, A., Sakov, A. and Zeltyn, S. 2001, Emprcal Analyss of a Call Center. Markby, D.E. 1995, "Makng telecommutng happen: A gude for telemanagers and telecommuters, Nlles, J. 2899

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