Calculation of railway transport capacity in an emergency based on Markov process

Journal of Beijing Institute of Technology, 2012, Vol.21, No. 1Calculation of railway transport capacity in anemergency based on Markov processMENG Xue-lei( 孟学雷)'2,日，JIA li-min(贾利民)”，QIN Yong(秦勇)”,XU Jie(徐杰)”，WANG Li(王莉)2(1. School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China; 2. State KeyLaboratory of Rail Trafe Control and Safety, Beijing Jiaotong University, Bejing 10044, China)Abstract: A method is proposed to calculate the railway transport capacity in an emergency to sup-port the dispatching work of control centers. The effect of an emergency on section transport capaci-ty is analyzed and the basic method to calculate the transport capacity is presented. The results showthat the situation-changing process in emergency is actually a Markov process. The calculation rule ispresented based on division of the time segment during which the emergency lasts. The algorithm isdesigned to calculate the transport capacity of each time segment. The pessimistic strategy and thefuzzy strategy are proposed to determine the computing value of the transport capacity of each timesegment, to satisfy the calculating requirements in different occasions. Our study shows that themethod is reasonable and practical and the method can be embedded in the train dispatching systemto support the operation work in an emergency.CLC number: U 292. 5Document code: A Article ID : 1004-0579(2012)01-0077-04The section capability of a railway is thetions, the minimal intervals between trains andmaximal number of trains that can go through thethe maximal speed that the section can support.section in a period of time (a day or an hour),The most important factor that affects the trans-with certain kinds of locomotives and cars, andport capacity is the maximal speed in the section.with a certain kind of organization rule. From theThere are three major methods to calculatedefinition, the section capability is related to thethe section capacity. An analytical method is de-equipments, such as locomotives and cars and thesigned to model the railway environment byorganization plan. In reality, the locomotives andmeans of mathematical formulae or algebraic ex-cars are relatively stable. So the section capabilitypressions'”-3. A simulation method simulates theis mainly determined by the organization rule andtrains’dynamic behavior of a system by moving itplan. The organization rules cover a series of or-from state to state in accordance with well-de-ganization constraints and leading principles ,fined rules to get the capacity'4-5]. An optimiza-such as the minimal running time through the sec-tion method is more strategic for solving the rail-vay transport capacity problem and providesReceived 2011-07-01Supported by the State Key Laboratory of Rail Traffic Controlmuch better solutions than purely analytical for-and Safety ( RCS2011K004 ); Beijing Jiaotong University ,mulae'6 71. In this paper, an analytical method isFundamental Research Funds of Gansu Province ( 620030 ) ;he National Natural Science Foundation of Chinaproposed, which is different from the methods in(61074151); Project of Research and Development on TrainControl Center Operation Expressing System of TubeRailRefs.[1 -3中国煤化工the' Markov( 306086 )匈Author for correspondence，associate professorprocess toMYHCNMHGlanges of seg-E-mail: foxred@ 163. comment capacity.-77-Jourmal of Beijing Institute of Technology, 2012, Vol.21, No. 11 Effect of an emergency on sec-ments, as shown in Fig. 1. The maximal speedsin each time segment are possibly different,tion capacitywhich leads to the different capacity.The transportation organization pattern, theSetratio between different types of trains and similarOt=t-t-,i=1 ,2,. ,N.(3)information are all uncertain. While we can notThencalculate the actual capacity, we can calculateCr= 2 a,(4)the transport capacity of the parallel train graph.An emergency compels the control center towhere a, is the actual section transport capacity ofadjust the speed constraint according to the de-the time segment i.gree of the emergency, which leads to the reduc-Although the lengths of every time segmenttion of the section capacity.are not the same because the length is determinedThe most popular formula to calculate theby the actual situation of the emergency, we as-transport capacity issume that they are the same in this paper. WeN:1 440 x60-(T。+T.)(1)will study the relation between the time segmentlength and the emergency in the future.where N is the capacity; T, is the skylight timeCwhich is reserved to do the maintenance workn(s); TW is the extra wasted time (s) and I is theinterval between two neighbor trains. So the cal-culation of I as shown below is the key point._L:+L.+L。 +Lpx3.6 +Tg,(2)where L, is the length of the train (m); L。is thelength of time segment that former train occupiesFig.1 Changing process of section in an emergency(m); L。is the length to assure the following train3 Calculating algorithmno to enter the section the preceding train occu-pies (m); L。is the braking distance (m); 0 isSuppose that there are M constraint speeds inthe average speed of all the trains( km/h), and T.an emergency in a railway. Relatively, there areis the additional time reserved for drivers to rec-M transport capacity values ( marked as C,2,""，ognize the signals. Different braking distancesCM and Cq