Estimation of average waiting time by using simulation & queuing analysis in radiotherapy section

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1 ISSN Etimatio average waiting time by uing imulation & queuing analyi in radiotherapy ection # Ihan P. Lade, # A. T. Wadgure, #3 P. K. Kamble, #4 V. P. Sakhare kavya9.ipl@gmail.com arvindwadgure@gmail.com 3 prahim.friend@gmail.com 4 vinod_akhare444@yahoo.co.in #34 Department of Mechanical Engineering, Datta Meghe Intitute of Engineering, Technology & Reearch, Wardha(MH), India ABSTRACT Queuing theory can be ued to predict ome of the important parameter like total waiting time, average waiting time of patient, average queue length. The imulatio queuing ytem can be applied to many real-world application. If it were poible to improve the queue, there would be more profit made and more time to carry out buine than ever before, which would be very ueful in thi fat paced world. Thi paper decribe the ue of queuing ytem to decreae the waiting time of patient. ARTICLE INFO Article Hitory Received: th February 6 Received in revied form : t March 6 Accepted: 3 rd March 6 Publihed online : 5 th March 6 I. INTRODUCTION Queue i a common word that mean a waiting line or the act of joining a line. It i formed when the number of cutomer arriving i greater than the number of cutomer being erved during a period of time. Long waiting lit or waiting time in public health i a notoriou problem in mot of the countrie all over the world. Thi paper decribe the ue of queuing ytem to decreae the waiting time of patient. Patient flow i a complex phenomenon becaue of the random nature of the arrival and ervice of the patient. Thi require a ytematic approach in planning. Queuing theory and imulation are analytical technique that are increaingly being accepted a valuable tool. Queuing ytem are quicker to ue however, they do not have the flexibility of imulation technique. It decribe the inter arrival time and ervice time of the patient coming to the hopital with a uitable ditribution. The primary input to thee model are arrival and ervice pattern. Thee pattern are generally decribed by uitable random ditribution. It i found that the inter arrival time of patient follow the Exponential ditribution, and the ervice time follow Normal ditribution. Queuing theory can be ued to predict ome of the important parameter like total waiting time, average waiting time of patient, average queue length. The queuing ytem predicted the average waiting time of patient, average queue length, cloer to the actual value. Queuing theory i a tochatic approach dealing with random input and ervicing procee. A there i a phenomenological analogy between a queuing ytem and the ytem in human, the aim of the preent tudy wa to apply queuing theory with Monte Carlo imulation.simulation i a mimic of reality that exit or i contemplated. Simulation i mot effectively ued a a tage in queuing analyi. The imulation i run for patient coming to department, the pertinent parameter like waiting time, ervice time, waiting time-ervice time ratio. Queuing Theory Queuing Theory i mainly een a a branch of applied probability theory. It application are in different field, e.g. communication network, computer ytem, machine plant and o forth. The Queuing Theory, alo called the Waiting Line Theory, owe it development to A. K. Erlang effort to analyze telephone traffic congetion with view telephone traffic congetion with a view to atifying the randomly ariing demand for the ervice of the Copenhagen automatic telephone ytem, in the year 99. The theory i ued in 5, IERJ All Right Reerved Page

2 ituation where the cutomer arrive at ome ervice tation for ome ervice, wait (occaionally not), and then leave the ytem after getting the ervice. In uch arrival and departure problem, the cutomer might be people waiting to depoit their electricity bill at a cah counter, machine waiting to be repaired in a factory repair hop, aero plane waiting to land at an airport, patient in a hopital who need treatment and o on. The ervice tation in uch problem are the cah counter in the electricity office, repairmen in the hop, runway at the airport and doctor attending the patient, repectively. In general, a queue i formed at a queuing ytem when either cutomer (human being or phyical entitie) requiring ervice wait due to number of cutomer exceed the number of ervice facilitie, or ervice facilitie do not work efficiently and take more time than precribed to erve a cutomer.the only way that the ervice demand can be met with eae i to increae the ervice capacity (and raiing the efficiency of the exiting capacity if poible) to the exiting level. The capacity might be built to uch high level a can alway meet the peak demand with no queue. But adding to capacity may be a cotly affair and uneconomic after a tage becaue then it hall remain idle to varying degree when there are no or few cutomer. A manger, therefore, ha to decide on an appropriate level of ervice which i neither too low nor too high. Providing too low ervice would caue exceive waiting which ha a cot in term of cutomer frutration, lo of goodwill in the long run, direct cot of idle employee (where, for example, the employee have to wait near the tore to obtain the upplie of material, part or tool needed for their work), or lo aociated with poor employee morale reulting from being idle. On the other hand, too high a ervice level would reult in very high et up cot and idle time for the ervice tation, thu, the goal of queuing modeling i the achievement of an economic balance between the cot of providing ervice and the cot aociated with the wait required for that ervice. Queuing Theory trie to anwer quetion like e.g. the mean waiting time in the queue, the mean ytem repone time (waiting time in the queue plu ervice time), mean utilizatio the ervice facility, ditributio the number of cutomer in the queue, ditributio the number of cutomer in the ytem and o forth. Thee quetion are mainly invetigated in a tochatic cenario, where e.g. the inter-arrival time of the cutomer or the ervice time are aumed to be random. hopital compried of patient inter arrival time and ervice time. The data collected i for the Radio therapy ection. The frequencie of patient are calculated and the ditribution for thi ection i plotted on the graph with inter arrival time and frequency a an ordinate a follow. A) DISTRIBUTIONS FOR INTER ARRIVAL TIMESINTER ARRIVAL TIME PROBABILITY DISTRIBUTION FOR RADIO THERAPY SECTION : The inter arrival time of patient viited the Radio therapy ection for 3 day i recorded and the frequency at fixed value of inter arrival time i calculated data collected a hown in the table..the graph i plotted between the inter arrival time and frequency of patient viited. The curve obtained reemble to the tandard exponential probability ditribution curve a hown in the fig... Hence it can be concluded that the inter arrival time for chemo therapy ection follow the exponential curve.it can be oberved that highet frequency 3 i at the 6 min. inter arrival time. But at 4 mi inter arrival time, the frequency i 64 (red point in fig...), thi recorded data omewhat deviate the ditribution curve from the exact exponential curve. Except thi 4 min. frequency 64, all other data fit to exponential ditribution a hown in the fig... from 3, gradually the frequency goe down approximately exponentially toward the lowet value at the inter arrival time of 4 min. hence it can be predicted that the mot of the time the patient come frequently with interval of 6 min.thi kind of frequency may lead for high waiting time. Table..Inter arrival time and frequency of patient for Radio Therapy ection. Inter Arrival Time Frequency (min.) Cae Study: Overview of Proce Daily, 7- patient (new and old) arrived in Chemotherapy ection. It een that, patient are wait in queue for a long time. Large Queue length een in the Chemotherapy ection. When the demand for a ervice exceed the capacity of that ervice, waiting i unurpriing and inevitable. So thi the large problem in the healthcare ector. Queuing ytem theorie have been ued to tudy waiting time and predict the efficiency of ervice to be provided. In thi department, problem i to be identified. Queuing theory and imulation technique i ued and optimum reource ued to reduced the average waiting time II. VALIDATION OF INTER ARRIVAL TIME AND SERVICE TIME PROBABILITY DISTRIBUTIONS Fig.. The inter arrival time ditribution for Radio Therapy ection. 5, IERJ All Right Reerved Page

3 A) DISTRIBUTIONS FOR SERVICE TIMES SERVICE TIME PROBABILITY DISTRIBUTION FOR RADIO THERAPY SECTION : The ervice time of patient viited to the Radio therapy ection for 3 day i recorded and the frequency at fixed value of ervice time i calculated data collected a hown in the table.the graph i plotted between the ervice time and frequency of patient viited. The curve obtained reemble to the tandard normal probability ditribution curve a hown in the fig... Hence it can be concluded that the ervice time for Radio therapy ection follow the Normal ditribution. Table. Service time and frequency of patient for Radio Therapy ection Service Time (min.) Frequency It can be oberved that highet frequency 3 i at the 6 min. ervice time. In the curve, gradually the frequency goe up and then down. It can be predicted that the mot of the time the patient come frequently with ervice time of 6 min. Thi kind of frequency may lead for high waiting time. Int er Arr ival Ti me 4 6 Arrival Time P r o Cu b. m. F re q Ran dom Pro b. No. Inter val Ditributio Service Time Se rvi ce Ti m e F re q. Prob C u m. Pr ob Ran do m. No. Inte rval A) AVERAGE WAITING TIME FOR RADIO THERAPY SECTION WITH PRESENTLY AVAILABLE MACHINE : The firt frequencie are calculated for each inter arrival time and probabilitie are calculated by dividing the each frequency by total frequency. The cumulative frequency i calculated a hown in the table 3.. Ditributio Inter Fig. The ervice time ditribution for Radio therapy ection. In all above mentioned ection the inter arrival time and ervice time ditribution have been dicued in detail. After identifying the probability ditribution the patient arrival and ervice time behavior can be predicted and the whole ytem can be imulated to find out the average waiting time by imulating the much more number of patient. III. CALCULATIONS OF AVERAGE WAITING TIME FOR RADIO THERAPY SECTION USING THE SIMULATION OF PATIENTS The imulation i done for 3 patient ( day) for the Radio therapy ection by uing the MATLAB program. Random number are generated and the interval i identified for the generated random number and accordingly the inter arrival time of the patient i decided ame i done for the ervice time. Preently the machine i available for providing the ervice. The aignment of patient to the machine i done by checking the availability of machine for next patient. Then the waiting time for each patient i calculated and average waiting time i determined.the average waiting time for Radio therapy patient i 7.9 min. and the average ervice time calculated i 3.3 min. A) AVERAGE WAITING TIME FOR RADIO THERAPY SECTION WITH ONE EXTRA MACHINE. In order to reduce the average waiting time of patient one extra machine i made available virtually in the MATLB program and the waiting time calculation are done according the tated procedure in the lat chapter. It can be identified that additio one machine to Radio therapy 5, IERJ All Right Reerved Page 3

4 ection ha reduced down the min. Thi indicate that the additio a machine ha reduced down the waiting time to zero i.e. no waiting at all. IV.RESULTS AND DISCUSSION :RESULTS DISCUSSION FOR RADIO THERPY SECTION The calculation done for the Radio therapy ection with ingle machine (preent) and machine (propoed) indicate that the additio one more machine ha reduced the average waiting time from 7.9 min to min i.e. no waiting time at all. From fig. 4. and 4. it can be concluded that the peak waiting time i min when ingle machine i available and it min when machine are available. Hence in the fig 5, the waiting time line i at zero level. in the table 5. and fig 5.. by allocating the extra reource a hown in the table 5. and fig. 5. Table 5. Compario average waiting time for each ection before and after the allocatio extra reource. Waiting Time (min) Sr. No. Section in Departme nt Radio Therapy Before reource After Reource 7.9 % Reduce d Table 5. Compario allocatio reource for each ection before and after the allocatio extra reource. extra reource Sr. No. Section in Departme nt Radio Therapy Before reource machine After Reourc e machine % Increa e in reourc e Fig 4.. Waiting time peak hour for Radio therapy ection with ingle machine Fig 5. Compario average waiting time for each ection before and after the allocatio extra reource Fig 4.. Waiting time peak hour for Radio therapy ection with two machine V.CONCLUSION average waiting time of patient for each ection in the radiation therapy and oncology department. The probability ditribution for patient arrival time and ervice time for radiotherapy ection have been calculated from the data collected and the average waiting time for the preent reource quantity and availability ha been calculated by imulating the number of patient uing MATLAB program. Then the extra reource are added e.g. one machine i added to Radio therapy ection. After adding the reource again the average waiting time ha been calculated for ection with extra reource. The objective i achieved by reducing the average waiting time of the ection a hown Fig 5. Compario allocatio reource for each ection before and after the allocatio extra reource Form the above figure and table following point can be concluded. 5, IERJ All Right Reerved Page 4

5 . The average waiting time for Radio therapy ection i reduced by if one more machine i added to the ection. and Communication (IJRITCC), vol 3 iue, Feb 5, ISSN REFRENCES [].Profeor Edward Anderon, A Note on Managing Waiting Line, UT McComb School of Buine. [].Sanih A. (June 7) Application Of Queuing Model And Simulation To The Traffic At New Mangalore Port, Department of Applied Mechanic and Hydraulic, NITK Surathkal. Karnataka. [3].Fatima Youef Abdalla Barham, (), Simulation in Queuing Model: Uing Simulation at Beit-eba croing check-point, Faculty of Graduate Studie at An-Najah National Univerity, Nablu, Paletine. [4].Wijewickrama A. K., Int.j.imul.model 5(6), 56-6, Simulation Analyi For Reducing Queue In Mixed-Patient Outpatient Department., Nagoya Univerity, graduate School of Economic & Buine Adminitration, Furo-cho, Nagoya, Japan. [5].Suan L. Albin, Jeffrey Barrett, David Ito And John E. Mueller, (99), A Queuing Network Analyi Of A Health Center, Department of Indutrial Engineering, Rutger Univerity, Picataway, NJ 55-99, USA. [6]. Samuel Fomundam, JeffreyHerrmann,(7), A Survey of Queuing Theory Application in Healthcare, ISR Technical Report 7-4, The Intitute for Sytem Reearch. [7].Sachin Jayawal & Gaurav Chhabra, (5), Simulation Study of an Inbound Call Center, Department of Management Science, Univerity of Waterloo. [].Igor Georgievkiy, Zhanna Georgievkaya, William Pinney (Alcorn State Univerity) Donald McWilliam (Texa Weleyan Univerity), Uing Queuing Analyi And Computer Simulation Modeling To Reduce Waiting Time In The Hopital Admitting Department. [9].Ozcan, Y.A., (6), Fir edition, Joey -Ba Publication, 6.Quantitative Method In Health Care Management; Technique And Application. [].Pieter Tjerk de Boer, geboren op januari 97 te Wildervank (gem. Veendam), Analyi and efficient imulation queuing model of Telecommunication Sytem. [].Ihan P. Lade., (3),.Simulatio Queuing analyi in hopital, International Journal of Mechanical Engineering and Robotic Reearch (IJMERR), Vol No 3, July 3, ISSN [].Ihan P. Lade., (5), Reductio waiting time by uing imulation & Queuing, analyi, International Journal on Recent and Innovation Trend in Computing 5, IERJ All Right Reerved Page 5