A Study of Queuing Model for Banking System

Transcription

1 Iteratioal Joural of Idustrial Egieerig ad Techology. ISSN Volume 5, Number 23), Iteratioal Research Publicatio House htt:// A Study of Queuig Model for Bakig System Toshiba Sheikh, Sajay Kumar Sigh ad Ail Kumar Kashya Chhatraati Shivaji Istitute of Techology Durg, Chhattisgarh, 49, Idia tsheikh99@gmail.com ; sajaysigh@csitdurg.i 2 ; ailkashya@csitdurg.i 3 Abstract Waitig lies ad service efficiecy are the imortat elemets for ay bak. Queuig theory has bee fairly a successful tool i the erformace aalysis of waitig lies. I this aer, a otimized model is roosed to imrove the bak ueuig system based o ueuig theory. This method ca otimize the umber of server ad imrove the service efficiecy that could effectively cut dow service costs ad customer s waitig time. Keywords Queuig system, Multi Server Queuig Model, Service efficiecy. Itroductio Waitig lies or ueues is the major source of difficulties to ay orgaisatio or service rovider istitutes like hositals, baks etc. Queuig theory basically a mathematical aroach, used for the aalysis of waitig lies. It deals with the roblems that ivolve waitig or ueuig). Queuig theory is used to aalysig the cogestios ad delays of waitig i lie. It is used to develo more efficiet ueuig system that reduce customer waitig time ad icrease the umber of customer that ca be served. Customers waitig time deeds o the umber of customers o ueue, the umber of servers servig lie, ad the amout of service time for each idividual customers. The time wasted o the ueue would have bee wisely utilized elsewhere oortuity cost of time set i ueuig). I a waitig lie system, whe cosiderig imrovemets i services to offer a otimal service level, cosider the cost of rovidig a give level of service agaist the otetial costs from havig customers waitig. Customer satisfactio is imroved by redictig ad reducig

2 22 Toshiba Sheikh et al waitig time ad adjustig staff. Prooses a icremetal aalysis aroach i which the cost of additioal servers is comared with the beefits it geerates. Servers are added util the icrease cost eual the beefits. Otimizatio Method Here the ueuig system is the Bak Service System. The followig assumtios were made for the ueuig system at the Pujab Natioal Bak Bilasur, i accordace with the ueuig theory: Poisso arrival rate of λ customers er uit of time. Exoetial service times of µ customer er uit of time. Queue discilie is first come first served basis by ay of the server. The waitig lie has two or more idetical servers. There is o limit to the umber of the ueue ifiite). The average arrival rate is greater tha average service rate. Followig otatio ad termiology are used i the formulatio ad evaluatio of the ueuig model: P = robability of exactly customers i the system. L s = exected umber of customers i the system. L = exected umber of customers i the ueue. W s = average time a customer seds i the system. W = exected waitig time of customers i the ueue. = umber of servers. C s = service cost of each server. C w = oortuity cost of waitig by customers. λ= the mea arrival rate exected umber of arrivals er uit time) of ew customers are i systems. μ= the mea service rate for overall systems exected umber of customers comletig service er uit time) whe customers are i systems. Model Formulatio All The model adotio i this work is the M/M/) : /FCFS) Multi Server Queuig Model. This is the exted form sigle server model where customer i a waitig lie ca be served by more tha oe server simultaeously. There are umbers of customers i the ueuig system at ay oit i time. If <, umber of customers i the system is less tha the umber of servers), the there will be o ueue. However, umber of servers will ot be busy. The combied service rate will the be μ = μ ; <. Ad, if umber of customers i the system is more tha or eual to the umber of servers) the all servers will be busy ad the maximum umber of customers i the ueue will be. The combied service rate will be µ = µ ;. Followig are the roerties of the Multi-Server Queuig Model:

3 A Study of Queuig Model for Bakig System 23 The robability of havig customers i the system is give by!! )!!) Exected umber of the customers waitig o the ueue. o L 2 ) )! Exected umber of customers i the system. L s L Exected waitig time of customers i the ueue. L W verage time a customer seds i the system. s s L W Utilizatio factor i.e. the fractio of time servers are busy. Cost Model I order to cost otimizatio ad determiatio of otimal umber of servers with the total otimal cost of the system, two oosig costs must be cosidered. These are: service cost ad waitig time cost. Exected Service Cost = C s ad Exected Waitig Time Cost i the system = λw s )C w By summatio of the service cost ad waitig time cost i the system we get, Exected Total Cost = C s + λw s )C w

4 24 Toshiba Sheikh et al Model Formulatio To evaluate the characteristics of the Multi Server Queuig System at the Pujab Natioal Bak usig TORA software. Takig, λ = 75 customers/hr., µ = 5 customers/hr. o the basis of these data the evaluatio is show i the Table. Table. Model Evaluatio of Multi-Server Queuig Model at the Pujab Natioal Bak Bilasur Sceario Lambda Myu System Utilizatio P o Ls L Ws i hours) W i hours) Total Cost/hr Fig.: Sashot of TORA Software Calculatio Fig.2: Exected Service Cost Vs Level of Service

5 A Study of Queuig Model for Bakig System 25 Fig.3: Exected Waitig Cost Vs Level of Service Fig.4: Exected Waitig Cost Vs Level of Service Fig.5. Exected umber of customers i the system L s ) Vs Probability of the system beig idle P )

6 26 Toshiba Sheikh et al Coclusio By the aalysis it is cocluded that as the service level icreases at a otimal service level, the waitig time of the customer is reduced, the service efficiecy is icreased ad the customer satisfactio is icreased ad as well as it is foud that at some secific umbers of service widows the total system cost is miimized. By the evaluatio it is roved that this otimal model of the ueuig is feasible. Refereces [] Huimi Xiao, Guozheg Zhag, The Queuig Theory Alicatio i Bak Service Otimizatio, IEEE, 2. [2] Gaurav Agrawal, A Queuig Model for Health Cetre, Iteratioal Coferece o Electroics ad Iformatio Egieerig ICEIE), 2. [3] Olaiyi, T.A. A Araisal of Cost of Queuig i Nigeria Bakig Sector: A Case Study of First Bak of Nigeria Plc, Ilori. Joural of Busiess & Social Scieces. Vol.9, Nos, &2, ages [4] X. X. Zhao. Queuig theory with the bak maagemet iovatio, Moder Fiace, No.3,.9-, 27. [5] Kostas, U. N., Itroductio to theory of Statistics, Mc-Gram Hill, Tokyo, 983. [6] Ndukwe, H.C, Omale, S ad Oauga O.O, Reducig Queues i Nigeria Bak Pharmacy. Africa Joural of harmacy ad harmacology Vol.58) [7] F. S. Hillier ad G. J. Lieberma, Itroductio to Oeratios Research, Tata Mc-Graw Hill, 8 th Editio, 27. [8] Chowdhury M. S. R., Rahma M. T. ad Kabir M. R., Solvig Of Waitig Lies Models i the Bak Usig Queuig Theory Model the Practice Case: Islamic Bak Bagladesh Limited, Chawkbazar Brach, Chittagog, IOSR Joural of Busiess ad Maagemet IOSR-JBM), Vol., Issue, , 23. [9] H. Zeg, Queue based o the cost of distributio systems, Joural of Wuha Uiversity of Sciece ad Techology, Vol. 3, Issue 3, , 27.