ࡱ> 5@ bjbj22 XX_*.8.8.899*@u22;====?A|A@DmFmFmFm;mps$rvRxs5Gf?j?"GGs==tPPPG:==DmPGDmPPZQeg=&;  L.8Jhfgu0@ufyNy4g**yg(ArC&PDE<AAAss**0.8fP"**.8 STOCHASTIC PROCESSES OF PORT'S BULK LOADING TERMINAL Mirano Hess, Svjetlana Hess Faculty of Maritime Studies Studentska 2, 51 000 Rijeka, Croatia e-mail:  HYPERLINK "mailto:dundovic@pfri.hr" hess@pfri.hr,  HYPERLINK "mailto:shess@pfri.hr" shess@pfri.hr Abstract Necessity for studying the processes in bulk cargo ports, which are the objects of research in this paper, follows from the fact that many real processes, which are characterized with unpredictability and changeability, are called stochastic because the parameters that determine these processes are the stochastic ones. In this paper the theoretical features of the Poisson process and a non-Poisson process, related to the queue will be given. This type of the queue, marked with M/D/1 by the Kendall notation, characterizes Poisson distribution of entity arrivals and deterministic distribution of service time. The main goal of this paper is to define port's bulk cargo terminal as the queuing system and then set up the appropriate model in which the loading terminal is determined as queuing system of type M/D/1. Subsequently, the model set up will be tested on the real example of the port's bulk cargo loading terminal in Bakar. On the basis of this model, the operating of the port can be determined with the purpose of making decisions for further running of the business. Keywords stochastic processes, queuing system M/D/1, loading terminal of the bulk cargo port INTRODUCTION Many real processes, which are characterized with unpredictability and changeability, are called stochastic because the parameters determining these processes are the stochastic ones. A part of the probability theory dealing with the stochastic processes is called the theory of stochastic processes. The queuing theory is one of the operational research methods dealing with the servicing processes of the entities that randomly arrive at the system and demand the service. By the mathematical models of queuing theory the interdependence between entity arrivals, waiting on service and their leaving the system are determined, with the purpose of system functionality optimization. The basic features of the queuing phenomenon are the mass character and random property, because the demand for service and the service time are stochastic variables. Through statistical data analysis on the number of ship arrivals per day and month of a chosen bulk cargo terminal, it has been established that no significant dependence exists in the sequence of daily arrivals of bulk ships, i.e. that arrivals are statistically random. From the previous statement, it follows that the number of ship arrivals can be taken as random variable and, in addition, the empirical distribution of this variable approximated with the appropriate theoretical distribution. The queuing theory can be applied in such cases for computing indices of port's bulk cargo terminal operations. In this paper the theoretical features of the Poisson process and a non-Poisson process, related to the queue will be given. This type of queue, marked with M/D/1 by the Kendall notation, characterizes Poisson distribution of entity arrivals and deterministic distribution of service time. The main goal of this paper is to identify port's bulk cargo terminal as the queuing system and then set up the appropriate model in which the loading terminal is determined as queuing system of type M/D/1. Subsequently, the model set up will be tested on the real example of the port's bulk cargo loading terminal in Bakar. Through application of the proposed model it should be possible to make decision on how to make optimization of the transhipment processes on a bulk loading terminal to increase its efficiency. THEORETICAL FEATURES The M/M/1 system is made of a Poisson arrival, one exponential (Poisson) server, FIFO (or not specified) queue of unlimited capacity and unlimited customer population. Note that these assumptions are very strong, not satisfied for practical systems (the worst assumption is the exponential distribution of service duration - hardly satisfied by real servers). Nevertheless the M/M/1 model shows clearly the basic ideas and methods of queuing theory. Next part summarizes the basic properties of the Poisson process and gives derivation of the M/D/1 theoretical model [6]. Most of the queue models that are not made of a Poisson arrival and exponential (Poisson) server, because of its complexity demand special approach. One of the models with Poisson arrivals and general independent service times has notation M/G/1. A modification of this model, with the assumption of constant service time is the model M/D/1, which will be used in this paper and applied at the real example. The Poisson process The Poisson process satisfies the following assumptions, where P[x] means "the probability of x": 1) P[one arrival in the time interval (t, t+h), for h 0] = lh+o(h), where l is a constant, t ( 0. 2) P[more than one arrival in the interval (t, t+h)]  EMBED Equation.3 . 3) The above probabilities do not depend on t ("no memory" property - time independence - stationarity). Let pn(t) = P[n arrivals in the time interval (0, t)]. Using the above assumptions 1) and 2), it is possible to express the probability pn(t+h), h 0: pn(t+h) = pn(t) [1 ( lh] + pn-1(t)l h (1') (n arrivals by t, no more arrival or n-1 arrivals by t, one more arrival) p0(t+h) = p0(t)[1 ( lh] (1'') (no arrival by t, no more arrival) The equations (1') and (1'') may be written in this way:  EMBED Equation.3 ,  EMBED Equation.3  . (2) Because of small h the terms at the left sides of (2) may be considered as derivatives:  EMBED Equation.3 ,  EMBED Equation.3  , that is:  EMBED Equation.3  ,  EMBED Equation.3  . (3) Equations (3) represent a set of differential equations, with the solution  EMBED Equation.3  , n=0, 1, 2, ... (4) Because of the assumption 3) the formula (4) holds for any interval (s, s+t) from R+. In other words the probability of n arrivals during some time interval depends only on the length of this time interval (not on the starting time of the interval). Number of arrivals Nt during some time interval t is a discrete random variable associated with the Poisson process. Having the probabilities of the random values (4), it is possible to find the usual parameters of the random variable Nt. Let E[X] be the mean (average) value, Var[X] the variance, and Std[X] the standard deviation of the random variable X:  EMBED Equation.3 , t(0 , (5) where (5) gives the interpretation of the constant l, that is the average number of arrivals per time unit. That s why the l is called arrival rate.  EMBED Equation.3  . (6)  EMBED Equation.3  . (6') Another random variable associated with the Poisson process is the random interval between two adjacent arrivals. Let X be the random interval. To find its distribution, let s express the distribution function F(x): F(x)=P[X < x] = P[at least one arrival during the interval x] = 1 - p0(x) = 1 ( e-lx. Because the interval is a continuous random variable, it is possible to compute the probability density as a derivative of the distribution function: f(x) = dF(x)/dx . Subsequently, distribution function of the random variable X is:  EMBED Equation.3  . (7) The distribution (7) is called exponential distribution, with parameter (>0. For the exponential distribution, probability density is:  EMBED Equation.3  . (8) If the random variable X is distributed by the exponential distribution with parameter (>0, then:  EMBED Equation.3 , EMBED Equation.3 ,  EMBED Equation.3  . (9) The expression (9) gives another interpretation of the constant l. Its inverted value is the average interval between arrivals. Like the number of arrivals, the distribution of intervals between arrivals does not depend on time. When applied to a service, the rate is called service rate (m). The parameter m is the average number of completed services per time unit (provided there are always customers waiting in the queue). Its inverted value 1/m is the average duration of the exponential service. The variance and the standard deviation can be computed by replacing l by m in the formulae (9). Unlike arrival, exponential service is an abstraction that is hardly satisfied by real systems, because mostly it is very unlikely to have very short and/or very long services. Real service duration will be typically "less random" than the theoretical exponential distribution. Another very important parameter of queuing systems is the ratio r of the arrival and the service rates called traffic rate (sometimes called traffic intensity or utilisation factor), representing the ratio between the arrival and service rate:  EMBED Equation.3  (10) The value of r shows how "busy" is the server. It is obvious, that for r  EMBED Equation.3  1 the queue will grow permanently. Therefore, the basic condition of the system stability is r < 1, for the cases with the unlimited customer population. NonPoisson models - type M/D/1 Most of the queue models that are not made of a Poisson arrival and exponential (Poisson) server, because of its complexity demand special approach. In these cases, simulation methods are being used with which it is relatively simple to simulate the process in the queuing model, or the analytical methods are being used. One of the models with Poisson arrivals and general independent service times, with the mean (average) value E[t] and the variance Var[t], t(0, has Kendall notation M/G/1. The inadequacy of this model is limitation regarding obtained results. It's impossible to compute the probabilities pn , therefore only basic parameters are being determined  the number of entities in queue LQ and in system L and the waiting time in queue WQ and system W . Let l be the expected number of Poisson arrivals, and service time distribution with E[t] and Var[t], where t is nonnegative random variable, t(0, then the model M/G/1 has following formulae [1, pp. 428]: ( the expected number of entities in system, known as Pollaczek-Khintchine (P-K) formula:  EMBED Equation.3 ,where l E[t] <1, t ( 0 , and by insertion the service rate =1/E[t] next is obtained:  EMBED Equation.3  , ( the expected number of entities in queue:  EMBED Equation.3  , ( the expected waiting time in system:  EMBED Equation.3  , ( the expected waiting time in queue:  EMBED Equation.3  . The modification of this model, with the assumption of constant service time is the model M/D/1. According to mentioned assumption Var[t] =0. In that case a Pollaczek-Khintchine (P-K) formula is simplified [1, pp. 430]:  EMBED Equation.3  , where =/, and  is constant rate of service. If the service time t is distributed by Erlang with parameters k and  (so E[t] =1/, and Var[t] =1/k2), which has notation by Kendall M/Ek/1, Pollaczek-Khintchine (P-K) formula transforms its form into following:  EMBED Equation.3  . The rest indices of the model are: ( average number of entities in queue:  EMBED Equation.3  , ( expected waiting time in queue:  EMBED Equation.3  , ( expected waiting time in system:  EMBED Equation.3  . For the system M/D/S, where S>1, the other formulae would be used [7 and 8]. MODEL FOR A PORT'S BULK CARGO LOADING TERMINAL In order to define port's bulk cargo loading terminal as the queuing system and then set up the model M/D/1 it is necessary to obtain basic features of the bulk cargo port, technical characteristics of the facilities in the port and describe working technology and organization. Basic features of the bulk cargo port Bakar The systems which functioning is subjected to random changes are analyzed by queuing theory. For analyzing port as a mass servicing system, the following is significant [3, p. 493]: - arrival time of ships can not be predicted with certainty, - servicing time, i.e. duration of transshipment, is random variable dependent on facility's capacity, transhipment line mechanization, ship deadweight, weather, and so on, - facility doesn't have constant working load since there are maintenance, inspection and repair breaks, breakdowns, breaks due to bad weather causing queues and intervals of low degree of utilization. Through analysis of present state of the facility the question that emerges is whether it is justifiable to invest in modernisation and reconstruction of the port in order to produce better business effects or it would be more appropriate to build a strategy for optimization of usage of existing resources. Through analysis of the bulk cargo port Bakar the next is observed [4, p. 54, 55]: - port is an open system since the ship entries are not part of it, - the bulk cargo port Bakar has two specialized quays for which ship queuing lines are eventually formed at anchorage, - unlimited number of ships waiting on service, - ships are patient clients, they don't abandon queue, - arrival rate is Poisson distributed which can be determined with statistical tests and is the most frequent case in practice, - servicing time, that is time that ship spends at the quay for loading has deterministic distribution because loading is continuous without breaks, - mutual assistance between loading and unloading terminals does not exist, - FIFO service rule is applied, without priority. Course of ship arrivals is stationary Poisson course with the following properties [3, p. 495]: - time independence, in arbitrary short time probability to arrive more than one ship is very small, i.e. ships enter the port one by one, - "no memory" property, arrivals of a ships are independent, - stationarity, intensity of a ship course is time independent since it is constant value dependent only on length of the observed period. For the bulk cargo terminal system, parameter ( represents the average number of bulk ships or quantity of bulk cargoes that arrive at the terminal during an observed time unit (e.g. during a year, month or day). However, in this paper arrival entities are the average quantity of bulk cargoes arrived by ships into port on yearly basis. The average number of bulk ships (in this case the average quantity of bulk cargo) that can be serviced in a time unit at certain berths is service rate (.. Table 1: Facility capacities of the bulk cargo terminal Bakar Quay Podboklength: 394 mmaximum depth: 18.5 mship: max 160,000 DWTStoragelength x width (m)capacity in tonsEquipmentiron orecoalPodbok330 x 27300,000100,000discharging equipment with conveyorDobra340 x 1980,00025,000conveyorPlato160 x 3680,00026,000unequippedCranescapacity in t/hyear of manufacturequantitydischarging equipment no.1 8001967.1discharging equipment no.2 1,6001978.1loading equipment  6002001.1storage conveyor 5001967.1Conveyorscapacity for iron ore1,600 t/hcapacity for coal1,300 t/hCapacities according to cargo type in tonsOreCoalsingle storage capacity in tons 400,000 150,000tech. capacity ship-storage for crane 45+16 t/shift 8,167 3,268tech. capacity ship-storage for crane 45 t/shift - 2,400tech. capacity storage-wagon for storage gantry crane in t/shift 2,500 -theoretical max. capacity in tons 4,960,000 3,000,000real capacity in tons 3,500,000 2,000,000technological-market capacity in tons loading terminal1,100,000 Source: Port of Rijeka [5] The ratio between arrival rate and service rate of cargo quantity is traffic rate or utilisation factor, that is traffic intensity of the berth ( ((=(/(). If (>(, one berth is insufficient as the employment rate is greater than 100%. In this event, the number of berths should be increased until service system is brought to stability condition, that is the system employment coefficient ( ( S< 1 has been satisfied. In practice, parameters values ( and ( are determined on the basis of empirical data or assessment depending on the goal and subject of research. Based on a definition of bulk cargo terminal as a service system and basic parameters of a terminal, operation indices of a loading bulk cargo terminal are computed. In this paper loading bulk cargo terminal Bakar, as part of port of Rijeka, has been analyzed. This terminal is capable to handle various types of bulk cargoes, iron ore, coal, bauxite, phosphate. Loading terminal has maximum degree of utilization for cargoes with bigger specific gravity, for example iron ore. Limiting possibility for expanding port capacities, so far as forwarding is concerned, rest on the number of stationed wagons per day. The amount of cargo transported by wagons amounts to 7,000 - 8,000 tons a day, and the maximum capacity of the wagon distribution center is 14,000 tons. The facility capacities are presented in table 1. Since the transhipment process consists of several technological operations (weighing of cargo, transport of cargo with conveyor from storage to ship, ship loading), the theoretical maximum capacity of loading terminal includes the maximum capacity of every single equipment that take part in transhipment (cranes, conveyors, distribution station, weighbridge, storage, wagons). Theoretical maximum capacity implies the maximum capacity of the equipment with the minimum capacity in transhipment chain. Terminal capacity is the maximum terminal capacity reduced for the cargo that has not been transhipped during breaks which includes breaks caused by mechanical failures of equipment, breaks caused by maintenance and cleaning of facilities, working breaks and time required for ship mooring and unmooring. Finally, quantity of cargo transshipped in port doesn't depend only on equipment, transport and storage capacities, but also on external factors. These are: - transport of cargo in port and out of port that depends on railway flow rate, flow rate of the railway hub and inland storages, - cargo demand, - breaks caused by weather or strikes. Technological-market capacity of the terminal includes the above factors, and is calculated taking into account the terminal capacity and several-years record of cargo flows. Modeling the port's bulk cargo loading terminal Bakar - queueing model M/D/1 Bulk cargo port in Bakar contains unloading and loading bulk cargo terminal. The procedure of loading cargo on ships consists of several technological processes: - cargo load with storage gantry cranes or bulldozer from storage on conveyor belts, - cargo transport by conveyors from storage to port's loading equipment, and - cargo load on ship. The assumption is that loading is continuous without any breaks and bottlenecks and for this reason loading time is constant. Subsequently, duration of ship service, i.e. time of ship's stay at the loading terminal, has deterministic distribution. From statistical data of port of Rijeka follows that the loading terminal's arrival rate of cargo (coal) ( is 918,518 tons for year 2005. It can be seen from table 1, that the yearly capacity of the loading terminal, representing the loading terminal service rate (, amounts to 1,100,000 tons (technological-market capacity). This data takes into account capacity of storage equipment and capacity of conveyors, which yearly capacity separately regarded is well over,. In contrast the storage capacity is here a key limitation factor. According to the queuing systems classification, the loading terminal is the queuing system with one service place and unlimited number of entities in queue, where service time is deterministically distributed with notation M/D/1/(. Consequently, the parameters for the observed model M/D/1/( are: ( cargo arrival rate (=918,518 t/year ( cargo service rate ( = 1,100,000 t/year According to the appropriate queuing theory formulae for this type of the queuing problem (see part 2.2.) the following terminal operation indices are computed: ( traffic rate (=(/(=0.835 ( mean  EMBED Equation.3 , ( variance  EMBED Equation.3 , ( the average quantity of cargo at the terminal (in queue and in loading process)  EMBED Equation.3 , ( the average quantity of cargo in queue waiting on ser7q   P Q b -3:;.0NRTؿ쬷옟uhVz6OJQJ]hVzOJQJ hVz6]hVz5CJ\ hVz5CJ hVz5\ hVz0JjhVzUjhVzUhVz0JmH sH jhVzUmH sH jhVzUmH sH hVzmH sH hVzhVz5;CJ$\ hVzCJ,78Tq  R S \ )}`$a$`\8 ~ n!"I"R"""#$h%%&'B'()e*``  ^ `TVTX68  (*,.02:<>BDFHJLN`b|~ ɪ hVzH*hVz6OJQJ] j-hVzhVzOJQJhVz6H*]jhVzEHUj5G hVzUVjhVzU hVz6]hVz jhVzC         " !!!!.!0!V!X!Z!\!!!""$"%"&"'"/"0"C"D"E"F"R"S"f"g"h"wmjhVzEHUjG hVzUVj hVzEHUjG hVzUVjhVzEHUjG hVzUVj^hVzEHUjG hVzUVjhVzEHUjsG hVzUVjhVzUhVz6OJQJ] j-hVz hVzH* hVz6]hVz*h"i"l"m"""""""""""""M#N#P#S#Z#[#\###$$$2$3$4$$$$$$%%4%5%d%f%h%i%|%}%~%%%%%&®¤®ˆ jhVzj]hVzEHUjG hVzUVhVz56\]hVz6H*] hVzH* hVz5\ hVz6]jhVzEHUjG hVzUVjYhVzEHUjG hVzUVhVzjhVzU3&&&&&&&&&&&&''('*','.'.(0((((((((((())) )h)j)v)x)z)|)~))))))))))#*6*e*f*g*⟓hVz6H*]hVz6H*OJQJ] hVzH* j-hVz hVzH*jhVzEHUjG hVzUVjhVzEHUjG hVzUVjhVzU hVz6]hVzOJQJhVzhVz6OJQJ]6g*h*m*n*o*p*s*t*v*w**********+ +!+G+Z+_+`+s+t+u+v+++++++++++++,,, ,&,(,N,jK'hVzEHUj G hVzUVj$hVzEHUj| G hVzUVj9"hVzEHUje G hVzUV jlhVz6]jhVzEHUjN G hVzUVjhVzUhVz6H*]hVz hVz6]0e*w***_+++&,f,2.B3,5n5d779;<<(>>>0?f???@8@``N,P,R,T,,,.......//000033 484:4^444444,5.5T5V5X5Z5555566(6*6,6.666d77999999޽޲ޝލ hVzCJj.hVzEHUjm9oB hVzUVj,hVzEHUjWB hVzUVhVzB*ph hVz5\ hVz6]hVz6OJQJ]hVzjhVzUj*hVzEHUj G hVzUV799f:h:l:; ;";@;B;;;;;;;;*<+<5<6<?<@<a<b<c<<<<<====>>>> >>>>l>n>x>z>>>>>>>>>2?4?Z?\?j6"G hVzUVj53hVzEHUj!G hVzUVjD0hVzEHUj!G hVzUVjhVzU jhVzhVz6OJQJ]hVz6H*] hVz6]hVz jhVz9\?^?`?f?h?????????@@2@3@4@5@@@AA(A)A*A+ABBBBB BBB~BBBBBBBBBBCCC"C$ClCnCDDD¸馜鱗 hVzH* hVzH*j7=hVzEHUj"G hVzUV hVz6]j;hVzEHUjU"G hVzUVj8hVzEHUj@"G hVzUV jhVzhVzjhVzUjL6hVzEHU68@A.AVBDD?DgDDDDDDKEzEFFtGG^H(I\JJJjKKKQL``DDDD?D@DgDhD{D|D}D~DDDDDDDDDDDDDDDDDFF0I8III[J\JJKTKLLLL9M@MFOGOQQ޷ޢޒގގމގގގގނx jmhVz6] jlhVz *hVzhs hVzCJjqFhVzEHUjP#G hVzUVjKDhVzEHUjH#G hVzUVjBhVzEHUjI#G hVzUV jhVzhVzjhVzUj?hVzEHUjJ#G hVzUV/QLL2MdMMPNNOkPQ Q QHQIQUQ $$$$Ifa$``Q QQIQTQQQqRwRRSRGRHRNR5( $$$If`kdpM$$IfTlr ?p# t064 laT$$$$If`a$ $$$$Ifa$NRWR^ReRpR$$$$If`a$ $$$$Ifa$$$$$If`a$pRqRxROC $$$$Ifa$kdmN$$IfTlAr ?p# t064 laTxRyRzRRRR $$$$Ifa$ $$$IfekdnO$$IfTl4p## t064 laf4TRRRRRRdWJ>> $$$$Ifa$ $$ $If $$$If`kdO$$IfTl\ xp# es  t064 laTRRRRRRdWJ>> $$$$Ifa$ $$ $If $$$If`kdP$$IfTl\ xp# es  t064 laTRRSSSSdWC77 $$$$Ifa$$$ $If`gds $$$If`kdQ$$IfTl\ xp# es  t064 laTSS.S3S9S;SdWJ>> $$$$Ifa$ $$ $If $$$If`kd^R$$IfTl\ xp# es  t064 laT;S*mHnHsHhVzhVzmHnHsHhVzhVzmHsHhVzhVz5;\mHsHhVzhV7 hi7hV72~` ^`$a$ Maritime Transportation Department, Faculty of Maritime Studies in Rijeka. Her field of interest is research of stochastic processes in traffic systems and their modelling. ISEP 2006  h%wCJmHnHuhV7(&P/ =!"#$%3 0&P/ =!"#$% P / 0&P/ =!"#$% / 0&P/ =!"#$% 3 0&P/ =!"#$% P / 0&P/ =!"#$% / 0&P/ =!"#$% 3 0&P/ =!"#$% P DyK dundovic@pfri.hryK 0mailto:dundovic@pfri.hrDyK shess@pfri.hryK *mailto:shess@pfri.hr Dd J  C A?"2k&Aﶓ-Br3Gi `!?&Aﶓ-Br3. h xcdd``gd``beV dX,XĐ IYRcgb ZS 憪aM,,He`Xvoav@Hfnj_jBP~nbC%@y mh vĚIL!& `I9 L0@3og)]Տ,w`lG #@w-ؤ .hXs$P 0y{1Ĥ\Y\ 1 u`uQrDd  J  C A?"25<p0i `! <p0``` :xڥTJ@UVA`*TςG+ڃPQm)x(^> YAT 4&Cj6o]!= ȧG^H4Bm!d vZmjMal)Ck;L &4'[b*1_Wɱ4 Fy$3"}QR!I#E U)CQVuq{iѻslG6l՟vRoR_e4$ŽrfKFUhIC.֝Nې xat'z оFyӘDd J  C A?"2ݷkFDL&%/i `!ݷkFDL&%/R `P:xڥSJP6X H}..l? uҍ[w?PFЅ  739's !H< '"D 9Ù:NP_]EB$ 3HhwEt-[J8IخՎm\0ʽ;vr& Jk6d{C':d㐤ubn}1 SA=cbшyI-Ӕ6n<̆o-l;Mvp2U< | \ |Ty柀w|W=i{s| Ut6ޣ3^Ƙ>،tJH\Mw_SˠzQ3ˍ!a~<xF1Sp ]uBl(7}dw~ z|Arnԧ'NiAQ2$.wZ}/e,Dd J  C A?"2G}l9Ec9i `!G}l9Ec9 `P:xڥTMKQTBEa`2hHEj "'2 ZO(e~B- 2޻ZL6sw!]?  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root Entry F@< L@FData |WordDocumentObjectPoolJ L@< L_1204294709F L LOle CompObjfObjInfo  #$%(+,-0347:;>ABCDEFILMNORUVY\]`cdgjknqrsvyz} FMicrosoft Equation 3.0 DS Equation Equation.39q,II '! h!0 0 FMicrosoft Equation 3.0 DS EqEquation Native H_1204297331Y F L LOle CompObj fuation Equation.39qII p n t+h()"p n t()h="p n t()+p n"1 t() FMicrosoft Equation 3.0 DS EqObjInfo Equation Native  _1204297349F L LOle CompObjfObjInfoEquation Native _1204297380 F LPH Luation Equation.39qѠPIġI p 0 t+h()"p 0 t()h="p 0 t() FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObjfObjInfoEquation Native (II 'lim h!0 p n t+h()"p n t()h="p n t()+p n"1 t() FMicrosoft Equation 3.0 DS Eq_1204297392FPH LPH LOle CompObjfObjInfo!uation Equation.39qI0I 'lim h!0 p 0 t+h()"p 0 t()h="p 0 t()WE FMicrosoft Equation 3.0 DS EqEquation Native "_1204297416"FPH LPH LOle &CompObj 'fuation Equation.39qѬhInI dp n t()dt="p n t()+p n"1 t() FMicrosoft Equation 3.0 DS EqObjInfo!)Equation Native *_1204297432$FPH LPH LOle .CompObj#%/fObjInfo&1Equation Native 2_1204297472;)FPH LPH Luation Equation.39qt(II dp 0 t()dt="p 0 t() FMicrosoft Equation 3.0 DS Equation Equation.39qOle 5CompObj(*6fObjInfo+8Equation Native 9ф II p n t()=t() n n!e "t FMicrosoft Equation 3.0 DS Equation Equation.39q_1204297610.FPH LPH LOle <CompObj-/=fObjInfo0?Equation Native @_1204297679,63FPH LPH LOle GCompObj24HfsȔII EN t []=n n=0" " t() n n!e "t =te "t t() n"1 n"1()!= n=1" " te "t e t =t_ FMicrosoft Equation 3.0 DS Equation Equation.39qII VarN t []=n 2n=0" " t() n n!e "t "t() 2 =tObjInfo5JEquation Native K_12042976968FPH LPH LOle P FMicrosoft Equation 3.0 DS Equation Equation.39qшIԧI StdN t []= VarN t []  = t CompObj79QfObjInfo:SEquation Native T_12042978061E=FPH L LOle WCompObj<>XfObjInfo?ZEquation Native [ FMicrosoft Equation 3.0 DS Equation Equation.39qxII F(x)=1"e "x xe"00x<0{ FMicrosoft Equation 3.0 DS Eq_1204297829BF L LOle ^CompObjAC_fObjInfoDauation Equation.39qt؟II f(x)=0xd"0e "x x>0{ FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native b_1204297852@OGF L LOle eCompObjFHffObjInfoIhEquation Native i_1204297941'LF L LOle lxԣII EX[]=te "t0" +" dt=1 FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjKMmfObjInfoNoEquation Native p_1204297940QFU LU LsȬInI VarX[]=EX 2 []"EX[]() 2 =1 2 FMicrosoft Equation 3.0 DS Equation Equation.39qOle tCompObjPRufObjInfoSwEquation Native xlII StdX[]= VarX[]  =1 FMicrosoft Equation 3.0 DS Equation Equation.39q$PIxI =_1113044507VFU LU LOle {CompObjUW|fObjInfoX~Equation Native @_1114585453T[FU LU LOle CompObjZ\f FMicrosoft Equation 3.0 DS Equation Equation.39q7LItI e" FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo]Equation Native ,_1204298170`FU LU LOle CompObj_afObjInfobEquation Native _1204298231^heFU LU LII L=Et[]+ 2 E 2 t[]+Vart[]()21"Et[]() FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObjdffObjInfogEquation Native PII L=+() 2 + 2 Vart[]21"() FMicrosoft Equation 3.0 DS Equation Equation.39q_1204298294jFU LU LOle CompObjikfObjInfol`wI8I L Q =L"Et[]=L" FMicrosoft Equation 3.0 DS Equation Equation.39q\\nIܢI W=L,Equation Native |_1204298304cwoFU L0 LOle CompObjnpfObjInfoqEquation Native x_1204298325tF0 L0 LOle W=W Q +1I FMicrosoft Equation 3.0 DS Equation Equation.39q@II W Q =L Q CompObjsufObjInfovEquation Native \_1204298389ryF0 L0 LOle CompObjxzfObjInfo{Equation Native p FMicrosoft Equation 3.0 DS Equation Equation.39qT\nItI L=+ 2 21"() FMicrosoft Equation 3.0 DS Equation Equation.39q_1204298570~F0 L0 LOle CompObj}fObjInfos`II L=+1+k2k1"() FMicrosoft Equation 3.0 DS Equation Equation.39qDIlI L Q =LEquation Native |_1204298569mF0 L0 LOle CompObjfObjInfoEquation Native `_1204298568F0 L0 LOle "Et[]I FMicrosoft Equation 3.0 DS Equation Equation.39qs@InI W Q =L Q CompObjfObjInfoEquation Native \_1204298576|F0 L0 LOle CompObjfObjInfoEquation Native @ FMicrosoft Equation 3.0 DS Equation Equation.39q$IxI W=L14 FMicrosoft Equation 3.0 DS Equation Equation.39q_1204300119Fb Lb LOle CompObjfObjInfoEquation Native _1204300144Fb Lp LOle CompObjfѬII Et[]=1=9.09"10 "7 year=0.0080hour FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoEquation Native _1204300239Fp Lp LOle ѸII Vart[]=1k 2 =8.26"10 "13 yearH"0hour FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjfObjInfoEquation Native _1204300288Fp Lp Lр}II L=+ 2 21"()=2.948tons FMicrosoft Equation 3.0 DS Equation Equation.39qp0IsI L Q =LOle CompObjfObjInfoEquation Native "Et[]=2.113tons FMicrosoft Equation 3.0 DS Equation Equation.39q|IPI L serv =L"L Q ==0.835_1204300310Fp Lp LOle CompObjfObjInfoEquation Native _1204300322Fp Lp LOle CompObjftons FMicrosoft Equation 3.0 DS Equation Equation.39qѴ}II W Q =L Q =0.02015hour=20.15h/1000tObjInfoEquation Native _1204300395Fp Lp LOle ons FMicrosoft Equation 3.0 DS Equation Equation.39qшII W=L=0.028hour=28h/1000 tonsCompObjfObjInfoEquation Native _1204300403Fp Lp LOle CompObjfObjInfoEquation Native  FMicrosoft Equation 3.0 DS Equation Equation.39qѸ JI W serv =W"W Q =0.00785hour=7.85h/1000tons     W !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVxE <"g,~ s_3rePaARЃ Pi5}Ψ wÒDd DJ   C A ?"2O,=&C@i `!O,=&C@<@ PVxڥKQgfwRJ!CdnACz :v0!u)S:Fۛgʮ}}f $KQT/! 뺲KMghS؋Ϋh-4)pݱR<:'ItzA'~vS4@ϪՈŎ9e=W\z]4PI MTJ -킦NkN+}蜥rۅ&~{Zru]>%i0 JuHzYa8Z']寤D4+'<4'V_N0o>K28uw$g^4eҫ7/&S6(2N&3$.Dd J   C A ?"2SV8i `!SV8`P.PxڥUkA~fn$[JZAPIdMdIy< @ڛ@M<{,ufvI7u&|{3%9}cw M"f/fNS# x[#6:62\:]6z4dBN.-,8-O0; nNs ϱ$=~ƒ1uDI[O@OB}L$8xL&9ŠS#j slIsál-F ;;4g+{e"faLX̅\YO+b{v.^V8"lǼeM7E5p}-9NJצ^B՗~f\^w񾨩A?n}ײƔ}JMr$cȫՌMK|65ou 8G.oNx 9uQ"p'cC8e9G*^ɫ~{Bzqq7׳* `'?M&$K2#*~VmkjMη{~}ƖSi6sQ|TiՐO1` HFmg"RN.C:|ŻW}!![&ugeR9Dd J  C A?" 2r-PXM N0i `!F-PXM `(PxڝTkQnjm"Rh9=\]^؀^=xP]ɘ񻿇^y}01&bel>\^PkOn \;W,7#VBxQz3U;[m ܏%~uDd |J  C A?" 2# PXEaCCy@i `! PXEaCCyn`0xڥT;KA#Ha2VIaD 1h0beaPX+ #w,7};{w&[ R &%DqT"mSsh`0ɣ/DyG|48-xz-_~+߉|s$Oq4ƟslCV VuC}2>IuJ\i*9#"lM}9%Ua< XR> [w#jN]':5)٫7^Wk{R͕NJN9_t\h0? eRV ·iJ-g*O]#=o,A] T_=5Lhp" V-=Ks I(׼R{L~y|Dd J   C A ?" 27?7٪ < i `!7?7٪ <~ `_PxڕK@{I[F BATbEMA?  -h N nf .^g?ޯﻻ X=d@> 1,3S B(xe'x@ԍsh q1N$D2\m1cDq`\/5<{~P,@u ZbuD|3cԔ.)~~-T_ [cѼWPtgu#_GS2ΗL_:Zv;T!@݁8ji4y-!Clr*YR(e9ѕyz5ZJ?(8;OU |TNRLwG TQ{~W~_ywDd 0lJ   C A ?" 2 3Ise}"i `! 3Ise~ H{xڕ;KAgf\  "⃔ʕ6Z"%B$|#}Fȹ39 XNRF^)]L/B b14u2#z7q9l-Ε1>X-v}Q L2(2isPu,O\޳ @ymI wh\Is x7v=t!P)&do]Pjb*5.Օۜ7?poz$zh[ܦu+7Zvg᱓.5U=N0#$q{XH,izO^ݟSp!41b<\$ |m9 0^oxDd P 0J  C A?"2w'ςdH`l'i `!w'ςdH`lkxڥKA{Uӥ"$(*0Cu阇Q))7;zu>1O5_~=]R_8j*睥*~u)avZ619s;-!iYk%HV{k[Qzy[<9Ɵʒ1¶nj5 Dd J  C A?"2Y?'gl̖up95,i `!-?'gl̖up9@ dxmQJA} *Hh? 6e !B20yo @]-:J5)aUU9S.׼;Yj:&ڨ\VOQb('4pq5,o¼a%Ҫ}>'>Shy,#0p5O(auQm?9)x/4s8z[ 헓r5hRN9SDd J  C A?"2riQa^ubaV.i `!riQa^ubaV@Rx5O ` ,N$n p/Pq(إ[GGq,5IK˅c}m)k)JdqUUihȂa\PD31B"2?{$pa`l_ Y,Ft=^D+^F2ukC3v"TžĮ,AhIE4"v,lXJFb քq1 Μ} G dfI3fY!,c&ahQS!pIXbD[a"SXI7‡9򥊮Mrntc3UYC:Od.+ħۆ,=-K']iԫ!@ֽC֮vnDd DJ  C A?"2mЀ=}6i `!mЀ=}\@ hrxڕRJA=s7,@1"NI#*j҉Ht~FB d{wg{3瞙QFׯMKJIFQYR9ɔH4y.][SC$d4聑 Zcj\lZ}Dd J  C A?"2])Mj?i `!])Mj6@ pdx}K@߽K6-Bq \B[Z!XRtg''"n pqҎN* {w? ɽ}߻q FBi/2&3 (E2:.|r ""&Q M;d8+MRsN4FVn0pwΑRZ-^dXvr/$j:Dd TJ  C A?"2>eFdQڼʩxUBi `!p>eFdQڼʩ 4 XJ>xcdd``gd``beV dX,XĐ I A?dm Wjx|K2B* R *3 vL@(\_({@Jv$^ `f:$ZZIPo]R2>p+I?6yInf XA\{"BρQ?C?XC_TΗ([.hǠv0y{)I)$5b6h&Dd H0J  C A?"2 ̷?dDi `!\ ̷?2@"k*x}QJ@}3Z 5z/ zG Z)jɹoRcueypܱ$uf;-aYGy76q_sR!].φE\ =XS̾)1D:wftLf<8X|sjҔONH]g7Ebnu(ˁjFOXMdDd J  C A?"2qgkyMFi `!Egky@@2 xuPJQ;<BHaP p3Br'Z"xXXoߙwefnnM ^؀?KZMzkQ&BMd&⟮~xM*W2[rXdςo?=u>3=(zqV j oYMhG)zCAjN~éeB'%(SmT9Nڰ2sPmppJKU\ ~nW$x]kM &Y挲Su"s/4r2O[>„|L/_F4=wbM 8}ŝG 0'н 1UtNu_d1Dd 3 XJ  C A?"2, qSѧ_i `!, qSѧ  xڕSKPwڠ8HqZ E@+.P!PV4݄';A\]U0jEjK;.O@@{&3 OɊȃBGyɊqQ( qIhLt& 0$HV4&c' +feݭO|ǥVҦ(Fu{T?#q_=16K#o }LAPJhE}jV k>֪Nyς:"OzP+Ʌ1\2us>4/P ]2d!ӌ.‚8F~?o?Q安$kqǢmR;@AԫB<##Fo'|]IfzZZgIZybvv mwWctͷP NFv~՘ lЅDd ` J  C A?"2t|[=-sEtai `!t|[=-sEt@@2xڍS=K`~bZAb]v]Z!`Z)/:+?MPhIK+҄7={I OGV 92iRQdJjU2eTa]Yh=5lECZ"РIA\;M<i7Y MҽbS6Ss=M|c!D EQ$nIIdW(U&N5؁I`)#"V*d%sNųt2n;F _WѲz#+rENJK^9 ხS>y!CA<=G#h觑xJ̓c~+3nexV`I&_M;:z7)sM^dA4@JvҪ)~ٟ?ک.3);)?8Ѵ$Iv?pXk'M:pMDd c TJ ! C A!?" 2>\N$UOfi `!>\N$UO XJQxڅRMJPI .ܵFЅ;=-LS=ww]3r8o(00|o7o [gD4H[%6<\Mp.?o UrYWe| X%z2.MehDdcH7byDd tXJ " C A"?"!2,4 Gb`/Bii `!,4 Gb`/B 0#}xڅRMJPƪA*p5t TDpa M*E+x@<Zf^Zl}a&C^^Ieb/%DJ 0ʞ!/KÞUJj!dX w0'v۬N=>kw ^Eq uYt`7<;z?hsP4X;ޕ6`o<WqAٴuJn:N&?nCqZeǭD+y_;IL#ǪFH|S )N8k}S?4^ @~yq`n*g:x#F=/}"S=: ҂F"Qt= ސ/hODd 0J # C A#?""2ߔBI0`?%a{ki `!ߔBI0`?%aPtkSx}RJ`$-͚v6\!PiV*tⓈ.ݗ fuSfI!j)I4qU3-¬B9JWjm-,${l3~iT7^9 ) =īwcD';kTnp#07xOY~WXq<M+xN};˖-RYP@|ItҾ_#0'?fͣf'TT2ϕm:Iٟ;gj]XA $jt'qjY\Dd TJ $ C A$?"#2wLa%K8ߩ)mi `!wLa%K8ߩ) `'XJ`xڅRJ@f[1D+ Pۋг- MSh)xoЗ w[MXo曙of!.  EQT8h. ^ `a$CJmHnHuVO2V ICT Section Headersd`5CJ6O26 ICT Text$a$CJ4@B4 Header  p#4 @R4 Footer  p#6U@a6 Hyperlink >*B*phPOrP 0BT1$dhxx`a$aJmHsHtHX>@X Title&$dh1$7$8$H$`a$5\aJtH~Or~ 0H1?$$$ & FEdhX1$7$8$H$^E`a$5;CJ\aJmHsHtHlOl 0List16$ PP:dh1$7$8$H$^P`:a$aJmHsHtHxOrx 0H2?$$$ & Fidhxx1$7$8$H$^`ia$;CJaJmHsHtH~Or~ 0H3I$$$ & F    dhxx1$7$8$H$^ `a$\aJmHsHtHP6@P List Bullet 2$ & Fa$mHsHN0@N List Bullet  & FaJmHsHtH\O\ 0List2%$ & Fdh1$7$8$H$a$aJmHsHtHFOqrF 0Formula $ b$`a$ V88<P2QR_*_'X78Tq    RS\ ) } l%6X{LD>axdv^~2!""##%&''-(j((((()6)Q)-*G*x*O+i+++++ ,0,K,,,- .../u011@222333444555e67U8V8W8888888888888 99999"9'9(9)90999A9I9m9n9t9}999999999999999999:::::9:@:F:H:I:\:a:g:i:j:{::::::::::::::::;; ;);2;;;<;p;w;~;;;;;;< <<<4<?<J<K<a<l<w<x<<<<<<s=z> ??x@y@>B5DgEFFFFoGG^HHIIJJ&LMPMgMxMMMFNWNcNkNNNNNOROkOOOP3PPPPPPPPPP1Q2Q:Q?QDQIQJQKQLQ^QpQqQsQ|QQQQQQQQQQQQQQQQQQQQQQQQQQQRRR RRRRR R&R,R-R0R=RCRKRLRNR[RaRhRiRoR|RRRRRS5W@WWYYYYYY-Z[[[[[[\ ]G]w]]]]]]]^~_________000p0000000M9000000000000 0 0 000 00 00M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900M900000000000000000000000000000000000000(0000000 0000000000M90D000M90D0 0 0 0 0 0 0 0 0 0 0 0 0  0  0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0` 0 0` 0` 0d 0` 0` 0` 0` 0d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0000 0000000000000000000000H000000000000000000000000M90v0 0000PM90v0a 0a 0a 0a 0d 0a 0a 0a 0a 0d 0a 0a 0a 0a 0d 0a 0a 0a 0a 0d 0a 0a 0a 0a 0d 0a 0a 0a 0a 0d 0a 0a 0a 0a 0d 0a 0a 0a 0a 0d 0a 0a 0a 0a 0d 0a 0a 0a 0a 0d 0a 0a 0a 0a 0d 0a 0a 0a 0a 0d 0a 0a 0a 0a 0d 0000000000000000000000000000000@0@0@0@0@0My000TQ T h"&g*N,9\?DQfa489:;<>?@BDbmn}e*8@QLUQQQQQQ R7RNRpRxRRRRS;SFSgSSSSS1TtTTT*UnU<_g$Bd<57=ACEFGHIJKLMNOPQRSTUVWXYZ[\]^_`acopqrstuvwxyz{|~6L`bk%'auw^rt &(""""##' ((j(~(((((( ) )7)K)M)-*A*C*O+c+e+++++,,1,E,G,kNNNNNNNOOROfOhOOOOP.P0PPPPPPP_XX::::::::::::::::::::::::::::::::::::@  @ 0(  B S  ?(  HB  C D_ 6$(6u _Hlt103058540 _Toc40680127 _Toc43533511 _Toc40680128 _Toc43533512 _Toc40680130 _Toc43533514 _Toc40680131 _Toc43533515 _Toc40680132 _Toc43533516 _Toc40680134 _Toc43533518 _Toc40680135 _Toc43533524####,,oGoG5W5W_@ ####,,GG?W?W_O  P | Q  <R S t <T . U d9 V W ̘ X ,, Y d+ Z ) [ 1 \ l3 ] N^ /_ ,` la b c d d Dn<e \7 f 4}Ag $o<h Li e j d k Te ' %::<<<???0J0JWWW ] ]]9]9]A^A^___      . %;;<<<???6J6JWWW]]]?]?]G^G^___   =*urn:schemas-microsoft-com:office:smarttags PlaceName=*urn:schemas-microsoft-com:office:smarttags PlaceType9*urn:schemas-microsoft-com:office:smarttagsStateB*urn:schemas-microsoft-com:office:smarttagscountry-region8*urn:schemas-microsoft-com:office:smarttagsCity9*urn:schemas-microsoft-com:office:smarttagsplace 8>ENq{ Xd03DG!)+:=QSSVkmqsC"N"##%%2&4&0'3''')))*****++. .e/q/0011V2[2558888)9/9<<-=8=????HBTBcCoC!D-DDDGGGGGG0J6JQQRRiRnRRRRRlUxUU VWWWWWW[[J]u]___bl  oq),7:Y[8>QS)+lp{}df2&6&''((-(0((((())G*L***++++,,..12B2E22222 3'33354;4555555L8Q8<<s=w=(>c>FFFFFF`HeHHHIIKKKKSMXMhMwM{MMMMINPNfNjNNNNNOOnOqOOO6P9PPPUU[[[[[[[\\ ]J]v]_____33333333333333333333333333333333333333333333333333333333333333333333D^zj((((()7)Q)+ ,1,K,8\:]::: ;*;<;q;;;;<<5<x<<<gMxMNNNOROkOOOP3PPP2QqQsQQQQQR5W@W[[J]v]]]_____J]u]___ PAVEL MESE PAVEL MESE PAVEL MESE PAVEL MESE PAVEL MESE Pavel MesemiranomiranomiranoHess 6<zn@4;kBGwU3UF-۾h+*Aԕ@N|vX+S!2 !gR|TU ^`OJQJo( hh^h`OJQJo(^`o(. ^`OJQJo(o pp^p`OJQJo( @ @ ^@ `OJQJo( ^`OJQJo(o ^`OJQJo( ^`OJQJo( ^`OJQJo(o PP^P`OJQJo(^`OJPJQJ^Jo(- ^`OJQJo(o pp^p`OJQJo( @ @ ^@ `OJQJo( ^`OJQJo(o ^`OJQJo( ^`OJQJo( ^`OJQJo(o PP^P`OJQJo(V^`VOJPJQJ^Jo(- ^`OJQJo(o pp^p`OJQJo( @ @ ^@ `OJQJo( ^`OJQJo(o ^`OJQJo( ^`OJQJo( ^`OJQJo(o PP^P`OJQJo(h^`.h^`.hpLp^p`L.h@ @ ^@ `.h^`.hL^`L.h^`.h^`.hPLP^P`L.hhh^h`.h88^8`.hL^`L.h  ^ `.h  ^ `.hxLx^x`L.hHH^H`.h^`.hL^`L. P:P^P`:OJQJo(- * * ^* `OJQJo(o   ^ `OJQJo( ^`OJQJo( ^`OJQJo(o jj^j`OJQJo( ::^:`OJQJo(   ^ `OJQJo(o ^`OJQJo(+HH^H`o(.+k^`ko(..+R ^`Ro(...+ xP ^ `xo(.... +  ^ `o( ..... +X ^`Xo( ...... +^`o(....... +8X^`8o(........ +`(^``o(.........7^7`OJPJQJ^Jo(- ^`OJQJo(o pp^p`OJQJo( @ @ ^@ `OJQJo( ^`OJQJo(o ^`OJQJo( ^`OJQJo( ^`OJQJo(o PP^P`OJQJo( 4;X+S+*AF-@NGwgR|T3 p66        P        (T                          8        |        V7s%wVz+W8888888888888 99999"9'9(9)90999A9I9m9n9t9}999999999999999999:::::9:@:F:H:I:\:a:g:i:j:{::::::::::::::::;; ;);2;;;<;p;w;~;;;;;;< <<<4<?<J<K<a<l<w<x<<<<2Q:Q?QDQIQJQKQLQ^QpQqQsQ|QQQQQQQQQQQQQQQQQQQQQQQQQQQRRR RRRRR R&R,R-R0R=RCRKRLRNR[RaRhRiRoR|RRRR_/@HP LaserJet 1100 (MS)LPT1:winspoolHP LaserJet 1100 (MS)HP LaserJet 1100 (MS)4C odterDINU"47#HP LaserJet 1100 (MS)4C odterDINU"47#u]u]g] u]u]@{0<<<< !"#%&()M*M+MO[]^_@ D@&(T@,.0246p@:x@>@B@@@@UnknownGz Times New Roman5Symbol3& z Arial?5 z Courier New;Wingdings"AhY&⢣&@?Q0@?Q0!24dO_O_ 3qH(?Vz A:\SEMI.DOTICT'02 Template%Manuscript for IEMT '97 in Austin, TX Paul WeslingHess4         rdDocWord.Document.89q