Research On Reducing The Cost of Stopping Port By Queuing Theory

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1 Research O Reducig Cost of Stoppig Port By Queuig ory Astract Ligyu Dog Merchat shippig college, Shaghai maritime uiversity, Shaghai 20306, Chia @qq.com With the developmet of gloal ecoomic itegratio, the im ad ex trade has ee icreased, ad a large umer of im ad ex trades have ee completed y sea. refore, the throughput of domestic s has ee icreasig.i order to allow the ship to otai a etter service i a shorter erth time, the erth operatig fee, ship's erth fee ad other related expeses icurred y the erth will e reduced. I comiatio with the queuig theory i operatios research, a reasoale modelig is made to the queuig pheomeo, ad the queuig system is plaed accordig to the erth. Keywords Throughput; Queuig theory; Modelig; Cost; erth.. Itroductio Port trade plays a irreplaceale role i the ecoomic eefit of compaies. I the trade, the order of the ship eterig ad leavig the ivolves the queuig process, how to make the 's cofiguratio facilities ad erths are fully used. reasoale umer of erths ca reduce the legth of the queue ad the time to eter the. umer of erths is too small, ad the waitig time of the ship will e prologed, the ship will ot uload i time, resultig i stagatio, ad the cost of the ship will ecome more; Too may erths are ot ideal, some erths are idle, o ship service is carried out, ad the related maagemet fees are still eeded, ad the ca ot get more profit. 2. Port throughput Accordig to the data of recet years, the throughput of our coutry is asically i the tred of cotiuous growth, ad it is kow that the is a ridge to guaratee the ecoomic relatios etwee coutries. 2. Compariso of data From the followig data, we ca clearly compare the period of 206 to 205, ad the chage of throughput asically shows the pheomeo of cotiuous growth. Port foreig trade throughput i205 moth Coastal s Ilad Yagtze river

2 Port foreig trade throughput i206 moth Coastal s Ilad Yagtze river Prolem of throughput disclosure icrease of throughput, the umer of ships i ad out of the will also e more, the ship has a series of operatios such as erthig, loadig ad uloadig. If the erth is full, the other ships that wat to come i eed to wait i lie, so that the caot meet the demad ad carryig capacity of the market, ad the time ad cost of waitig for the ship will icrease. So i order to solve this prolem, the we use queuig theory i operatioal research modelig, ratioal plaig, or of the ship, shorte the waitig time of ships, ad compare to the ship dock cost calculatio. 3. Queuig theory model costructio to solve the ship's waitig. 3. Relevat kowledge of queuig theory Queuig theory is a theory rach i operatioal research, is a specialized research due to the ifluece of radom factors ad the crowdig of sciece, also kow as the theory of stochastic service system, has ee widely used i all aspects of life. I reality there are a umer of services will face lie, such as supermarket queue to pay for items, register queue to see a doctor i a hospital, waitig i lie to uy tickets, us statio ticket office, etc., queuig for uses will e produced due to the radomess of the customer arrival ad service time queuig pheomeo, eve appear crowded pheomeo. Queuig theory is to study, how to esure the quality of services uder the premise of maximizig efficiecy of service, amely: use mathematics method to study how to determie the most appropriate umer of service persoel ad equipmet, to otai good quality of service, service costs the least. so called related cocepts, i each of the differet queuig system, its customers are accept service people, thigs, ad give the customer service people, thigs, (system) ito the receptio desk. Queuig system, each customer y the customer source i a certai way arrive service system, first joied the queue queue wait for service, choose the customer service desk accordig to certai rules from the queue for service, service customers to immediately. Geerally, at least oe of the arrivig time itervals ad service hours is radom. Are ivolved i the queuig theory kowledge of the proaility theory, the queuig system, customers have arrived at itervals with service time distriutio are maily egative expoetial distriutio, poisso distriutio, Erlag distriutio. 3.2 Queuig modelig of ships. Accordig to the queuig theory i operatios research, ship queuig is also a dyamic stochastic system. Make sure to the of shippig for the customer, reward erth as the service desk, ad the queue for a ifiite umer of customers waitig i lie, so, ship ad provide hadlig erth ad achorage for waitig for shippig lie costitutes a radom service system. Due to the radomess of the ship to the, the sigle team ad the parallel multi-service platform (the service umer is ) are adopted, amely M/M/ model; Similar to the stadard M/M/ model, the ship queuig service time is hadled whe the erth umer is. I the M/M/ model, the rules are still keeps cosistet, the differece is that of vessel arrival process said the first M oey the poisso distriutio, 66

3 said the service time of the secod M oey expoetial distriutio, (ecause whe service time oey egative expoetial distriutio, the uit of time to complete ship dock loadig ad uloadig of goods or service rate ca oey the poisso distriutio, so the secod ad first said are M), the third idicates the ca e docked o the umer of erths. Its queuig rules are first to first served, ad the time iterval distriutio ad service time of ships are radom. This requires kowledge i proaility theory. I this model, the work of erths is idepedet of each other ad the average service rate is the same. average service rate of the whole service orgaizatio is. service rate of the queuig system ad systems related to the ship to the Numers, whe the queuig system of the ship to the umer is ot greater tha the umer of erths, amely s, or less or less all the erth system of a ship, the system of service rate for s; Whe the umer of ships i the system is s >, ships have ee docked i the erth, ad the remaiig vessels are waitig for service i the achorage, the service rate of the system is. I order to etter solve the state proaility of the system, the diagram elow is the state trasfer diagram of the system, which is easy to uderstad. Vessel arrival Queuig service Service desk (related services) From this diagram, we ca use the relevat mathematical formula to solve it. Get system status 0,,2...,,... stale proaility equatio. P P =P ( ) =( ) (=,2,3,,) P P =( ) (=+,+2, ) P P Ad we ca solve it y the aove equatio 0 P s (!!! P =. ) s ( ) P p ( ) 67 ()! -ρ 0 0 > Usig these formulas to otai the results, the umer of M/M/ queuig system is otaied y usig the same method as the sigle service desk system, as follows: () average umer of ships i the queuig system. d ρ Ls d P dρ L d q s0 d 0 (2) average umer of ships queuig i. -

4 ( ρ) ρ L q ( ) P 2!( ρ) (3) average legth of stay i the queuig system is the time whe the ship arrives at the util the service is completed. Ls W s W q (4) average time spet i the queue is equal to the expected value of the time spet i the system mius the expected value of the service i the system. W W q s 3.3 Case aalysis Next, take wezhou as a example to simulate the queuig system. Sice aciet times, wezhou has ee a tradig, located o the southeast coast, with advatageous geographical locatio ad audat resources, ad is the most imat trasatio hu. re are 6 erths i wezhou for loadig ad uloadig operatios, ad the s are divided ito differet operatio areas. cargo trade etwee wezhou ad may coutries, such as South Korea ad Hog Kog, has opeed up differet routes to igo ad Shaghai, ad the throughput has ee icreasig year y year. Tale throughput ad erthig of the i wezhou i Time/moth total umer Throughput/ TEU Berthig quatity/vessels Accordig to a data tale, a total of 2009 wezhou ca e foud o the umer of ships docked for 448 ships, the throughput of each moth has a growig tred, visile wezhou to provide ship dock erth, ad efficiet use of achorage, resources, reduce vessel i achorage queue waitig time at the same time, take advatage of all coditios of maximizatio. Tale 2 Calculatio of related quatitative idicators. Compariso of type Ship to rate Chael service rate average of queuig ships(ship) Average of ships.(ship) Queuig time(d) mea time of ship erth.(d) 5 erths erths erths O the asis of previous throughput data, whe differet ship types are queuig through s, the relevat data from the aove tale ca e used to determie the dockig coditios whe differet erths are set up i the. Queued to service the umer of ships i the, the system reached i the average umer of ships, shippig lie average waitig time, shippig, the average time these through the statistics ad calculatio, ad familiar with the whole process of system, the idicators to judge the system wait i lie. It ca e foud that the more erths, the reasoale utilizatio of the ifrastructure equipmet; shorter the average queuig time, the higher the service efficiecy of the system ad the faster ad faster operatio of the whole. 68

5 Differet s have differet chargig stadards for differet types of ships ad toage. Ships, ad roads durig the to use the equipmet, waterway, erth, loadig ad uloadig operatio of the service ad pay the relevat expeses: i accordace with state regulatios of ship pilotage, tug, erthig, light ad to hadle the goods produced y hadlig fees, tallyig fees, etc., ad some miscellaeous fees. shall ot e charged for dockage if the ship is ot i its ow right, as log as it is ot its ow cause. Docked at the of achorage avigatio of the ship, the ship i wharf erthig, i excess of the prescried time still parked dock should e charged fees, so, ship will e caused y queue waitig time of eed to pay more fees, i order to ecoomic eefit, eed to the erth of reasoale arragemet. 4. Coclusio M/M/ model is adopted to traslate the queuig pheomeo of ships ito the prolems solved y mathematical method, which proves the imace of comiig theory with practice. This model accordig to the umer of erth to resource utilizatio with explaatio, ut is ot eough, this model also eeds to optimize adjustmet, uder the coditio of differet throughput, chage the model part of the lik, dealig with differet evets. Refereces [] guo qiag, su hao. Operatioal research priciples ad algorithms. [M]. Beijig: sciece press, [2] huag xiao-mig, xu xiaoyi. Applicatio of queuig theory i plaig ad desig [J]. Joural of Qigdao uiversity, 996.(3): [3] luo rogjia. Queuig model ad its applicatio. [M] huazhog uiversity of sciece ad techology press, 990. [4] shao jugag. of operatio of yagsha area through capaility [J]. Joural of Shaghai maritime uiversity, (4) [5] wu zhaoli. Maritime traffic egieerig [M]. Dalia: dalia maritime uiversity press,

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