{"id":1094,"date":"2020-11-17T11:52:10","date_gmt":"2020-11-17T11:52:10","guid":{"rendered":"https:\/\/wordpress.peters-research.com\/?page_id=1094"},"modified":"2020-11-17T16:36:51","modified_gmt":"2020-11-17T16:36:51","slug":"the-theory-and-practice-of-general-analysis-lift-calculations","status":"publish","type":"page","link":"https:\/\/wordpress.peters-research.com\/index.php\/papers\/the-theory-and-practice-of-general-analysis-lift-calculations\/","title":{"rendered":"The Theory and Practice of General Analysis Lift Calculations"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1094\" class=\"elementor elementor-1094\">\n\t\t\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-2bd44fca elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-eae-slider=\"50535\" data-id=\"2bd44fca\" data-element_type=\"section\" 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class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-624c56e elementor-widget elementor-widget-heading\" data-id=\"624c56e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">The Theory and Practice of General Analysis Lift Calculations\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-550f1783 elementor-widget elementor-widget-text-editor\" data-id=\"550f1783\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>R D Peters BSc<br>Ove Arup &amp; Partners<\/p>\n<p><em>This paper was presented at ELEVCON Amsterdam 1992, The International Congress on Vertical Transportation Technologies and first published in the IAEE book &#8220;Elevator Technology 4&#8221;, edited by G.C. Barney. It is reproduced with permission from The International Assocication of Elevator Engineers.&nbsp;<\/em>&nbsp;<em>This web version \u00a9 Peters Research Ltd 2010.<\/em><\/p>\n<h3>Abstract<\/h3>\n<p>The formulae presented in this paper allows analysis of any peak passenger traffic flow for any practical configuration of lifts.&nbsp; This means that we can consider not only a typical office morning up peak, but also shopping centres, office blocks with underground car parks and roof top restaurants, etc &#8211; scenarios not dealt with by traditional lift traffic analysis methods.&nbsp; Derivation of the formulae and their implementation on a personal computer are discussed.&nbsp; Practical applications are demonstrated using the Oasys LIFT program which utilises the General Analysis formulae.&nbsp; Examples are taken from projects on which the author has advised.<\/p>\n<h3>1.&nbsp; Introduction<\/h3>\n<p>Many engineers designing with the help of computers have a healthy scepticism of complex computer models which sometimes give unrealistically precise predictions of our imprecise world.<\/p>\n<p>But it is possible and worthwhile to learn about the effects on lift service of any passenger lift traffic flows where they can be predicted for a new building or measured in an existing building.<\/p>\n<p>Analytical lift calculation procedures generally address specific passenger traffic flows.&nbsp; An up peak analysis describes the morning incoming peak in an office building, a down peak the reverse.&nbsp; A two way peak describes a combination of up and down peak traffic (e.g. the traffic flow in a multistorey car park).&nbsp; The interfloor analysis allows passengers to arrive at any level, but assumes their destinations are always in proportion to the individual floor populations.&nbsp; Each of these traffic flows are solely special cases for the General Analysis procedure described in this paper which, when implemented on a computer, allows analysis of any peak passenger flow for any practical configuration of lifts.<\/p>\n<p>Before considering the General Analysis formulae we must first define our measure of passenger traffic.&nbsp; The term commonly applied in an up peak analysis, the Five Minute Ratio, cannot describe fully the traffic we wish to define.<\/p>\n<h3>2.&nbsp; Defining lift passenger traffic<\/h3>\n<p>The author&#8217;s introduction to lift traffic analysis was through writing a lift simulation program, as noted in the biography of this paper.&nbsp; Any analytical analysis for the general case must define lift passenger traffic in a similar way to simulation models, identifying the rate of passenger arrivals at each lift landing station and the passengers&#8217; probable destinations.&nbsp; To define the passenger flow completely we need two terms:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image001.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the passenger arrival rate at floor i (defined for each floor at which passenger may arrive)<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image003.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; the probability of destination floor of passenger from floor i being the jth floor (defined for all possible i and j)<\/p>\n<p>It is easier to show these terms diagrammatically.&nbsp; For example the simple case of an up peak traffic flow in an office block could be as shown in figure 1.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/thetheoryandpracticeofgeneralanalysisliftcalculations\/figure%201%20passenger%20traffic%20flow.jpg\" alt=\"\" width=\"469\" height=\"271\" border=\"0\"><\/p>\n<p><em>Figure 1&nbsp; Example passenger traffic flow for a typical office up peak<\/em><\/p><em>\n<\/em><p><em><\/em><br>A more complex traffic flow such as may be found in a shopping centre with car park above could be as shown in figure 2<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/thetheoryandpracticeofgeneralanalysisliftcalculations\/figure%202%20passenger%20traffic.jpg\" alt=\"\" width=\"510\" height=\"273\" border=\"0\"><\/p>\n<p><em>Figure 2 Example Passenger Traffic Flow for Shopping Centre with Car Park above<\/em><\/p>\n<h3>3.&nbsp; Principles of derivation<\/h3>\n<p>Having defined passenger traffic we can apply our mathematical model.&nbsp; It is not the intention of this paper to give a line by line derivation of the formulae, but to establish the basic principles and assumptions.&nbsp; The complete set of formulae and definitions are given in the appendix of this paper.&nbsp; The formulae were first published by the CIBSE Building Services Engineering Research and Technology Journal in 1990<sup>1<\/sup>.<\/p>\n<p>Before we write down the formulae we must define one more term:<\/p>\n<p><em>Pij<sup>(n)<\/sup><\/em>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;Probablility of n passengers travelling from the<em>&nbsp;i<\/em>&nbsp;th to the&nbsp;<em>j<\/em>&nbsp;th floor in the time interval&nbsp;<em>T<\/em><\/p><em>\n<\/em><p><em><\/em>It is generally accepted that the arrival of passengers at a lift landing station is reasonably approximated by a Poisson process<sup>2<\/sup>.&nbsp; This gives us the result:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image013.png\" alt=\"\" border=\"0\"><\/p>\n<p>When dealing with probabilities it is generally easier to calculate the&nbsp; probability of an event not happening, and subtract that result from 1 to find the probabiity of the event.&nbsp; So, if we let<\/p>\n<p><em>P<sub>ij<\/sub><\/em>&nbsp;=&nbsp;<em>P<sub>ij<\/sub><\/em>(0)<\/p>\n<p>we get:<\/p>\n<p><em>P<sub>ij<\/sub><\/em>= exp(-\u00b5<em><sub>i&nbsp;<\/sub>Td<sub>ij<\/sub><\/em>)&nbsp;<\/p>\n<p>The probability of the lift stopping at the jth floor on its journey up is:<\/p>\n<p>1 &#8211;&nbsp; (probability of no calls from lower floors to the jth floor) * (probability of no calls from the jth floor to higher floors)<\/p>\n<p>Mathematically, we can express this:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image019.png\" alt=\"\" border=\"0\"><\/p>\n<p>Applying this and similar principles we can derive<\/p>\n<p>S&nbsp; the probable number of stops in a round trip<br>L&nbsp;&nbsp;the probable lowest reversal floor<br>H&nbsp; the probable highest reversal floor<\/p>\n<p>For more complex problems where lifts do not serve all the same floors, or are of different speeds, capacities, etc we must define &#8220;overlapping zones&#8221; where passengers are likely to take the first lift that arrives and serves their destination floor.&nbsp; The formulae allow us to calculate the split of traffic between overlapping zones for each possible journey from the ith to the jth floor.<\/p>\n<h3>4.&nbsp; Computer implementation<\/h3>\n<p>A standard IBM PC or compatible has sufficient computing power to calculate a solution for a typical lift configurtion within seconds.<\/p>\n<p>Implementation of the method is relatively straightforward for someone with experience of lift traffic analysis and computer programming.&nbsp; As is the case for many analytical programs, writing the user input\/output routines can be the most difficult and time consuming task.<\/p>\n<p>The calculation is iterative as the equations for probable number&nbsp;of stops and reversal floors are dependant on the Waiting Interval and vice-versa.&nbsp; the procedure here is to &#8220;guess&#8221; the Waiting Interval, revising the guess for each iteration until the guess equals the result.<\/p>\n<p>The flow chart in figure 3 defines the main program structure and subroutines.<\/p>\n<p>A further iteration is required if overlapping zones are defined as the calculation for splitting data between zones is dependant on the Waiting Interval of each zone and vice-versa.<\/p>\n<h3>5.&nbsp; The Oasys LIFT program<\/h3>\n<p>The Oasys (Ove Arup Computing Systems) LIFT program has been used on a wide range of projects throughout&nbsp;the international Ove Arup Partnership since its first issue in 1989.<\/p>\n<p>The program is written in Fortran 77 with the help of Oasys standard input\/output routines and run on PC&#8217;s.<\/p>\n<p>In addition to basic implementation of the General Analysis method, the program offers the user additional features:<\/p>\n<ol>\n<li>the computer automatically calculates destination probabilities for specific passenger traffic flows such as up peak, down peak, two way and interfloor when selected by the&nbsp; user<\/li>\n<li>for the defined passenger traffic, the program will allow analysis over a range of possible solutions in a single analysis run (e.g. 3 to 4 lifts, 1.6 to 2.5m\/s, etc)<\/li>\n<li>a traditional up peak analysis calculation procedure is included and allows users to compare results and confirm consistence before considering more complex traffic flows with the General Analysis method<\/li>\n<\/ol>\n<p>From the users viewpoint there is one main difference between using the traditional (OLD) and General (NEW) calculation procedure for an up peak analysis:&nbsp; in a traditional analysis you would normally assume that the lift was 80% full and calculate the resultant Five Minute Ratio.&nbsp; Using the General Analysis method the Five Minute Ratio is defined and the&nbsp;program determines how full the lift is as a result of this passenger traffic.&nbsp;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/thetheoryandpracticeofgeneralanalysisliftcalculations\/fig%203%20flow%20chart.bmp\" alt=\"\" width=\"439\" height=\"626\" border=\"0\"><\/p>\n<p><em>Figure 3&nbsp; Program Flow Chart<br><\/em><br>The second approach is more helpful as specifiers often choose larger lifts than required for reasons of prestige, etc which if assumed 80% full give unrealistically high Five Minute Ratios and Waiting Intervals.&nbsp; The General Analysis just notes how full the lift is for the given Five Minute Ratio.<\/p>\n<p>One occasional user problem is that zero Waiting Interval and Capacity Factor results are given when the program is asked to analyse an over-lifted solution.&nbsp; If there is insufficient traffic to keep the lifts busy, in effect there will normally be a lift left waiting at the main terminal floor unused &#8211; the iterative value of Waiting Interval tends to zero, as would be the case in real life.<\/p>\n<h3>6.&nbsp; Examples<\/h3>\n<h4>6.1 A typical office up peak analysis<\/h4>\n<p>A prestigious office block in London with ground floor and eight upper stories.&nbsp; Floor populations range between 50 and 100 persons per floor.&nbsp; A stair factor of 50% (50% walk one floor, 25% two, 13% three, etc) has been assumed.<\/p>\n<p>The morning up peak is likely to be the busiest time for the lifts.&nbsp; A five Minute Ratio of 17% is assumed based on the possiblity of an unified tenancy with the majority of employees starting work in the morning at approximately the same time.<\/p>\n<p>The user enters the data, selecting the up peak analysis (so not needing to define destination probabilities which are in proportion&nbsp;to the population of each office floor).&nbsp; The lift analysis selection criteria is set over a range of numbers of lifts, capacities, speeds, etc with limits defined for the maximum Waiting Interval and Capacity Factor acceptable.<\/p>\n<p>Each configuration is analysied, rejected or displayed dependant on whether or not the selection criteria are met.&nbsp; The user selects his preferred solution from the output, in this case:<\/p>\n<p>No of lifts&nbsp;&nbsp;&nbsp;&nbsp; 3<br>Contract Speed&nbsp;&nbsp;&nbsp;&nbsp; 2.0m\/s<br>Lift Capacity&nbsp;&nbsp;&nbsp;&nbsp; 1000kg<br>Probable No of Stops&nbsp;&nbsp;&nbsp;&nbsp; 6.4<br>Probable Highest Reversal floor&nbsp;&nbsp;&nbsp;&nbsp; 7<br>Waiting Interval&nbsp;&nbsp;&nbsp;&nbsp; 30s<br>Capacity Factor&nbsp;&nbsp;&nbsp;&nbsp; 70%<\/p>\n<p>For this &#8220;simple&#8221; case the user could compare results with the alternative, traditional up peak analysis.&nbsp; Here the default Capacity Factor is 80% and the Five Minute Ratio is calculated as&nbsp;opposed to input.&nbsp; The results are as follows:<\/p>\n<p>No of lifts&nbsp;&nbsp;&nbsp;&nbsp; 3<br>Contract Speed&nbsp;&nbsp;&nbsp;&nbsp; 2.0m\/s<br>Lift Capacity&nbsp;&nbsp;&nbsp;&nbsp; 1000kg<br>Waiting Interval&nbsp;&nbsp;&nbsp;&nbsp; 33s<br>Five Minute Ratio&nbsp;&nbsp;&nbsp;&nbsp; 18%<\/p>\n<p>The results are very similar for both analysis methods.&nbsp; The second set of results have marginally higher Waiting Interval and Five Minute Ratio, but this corresponds with the lift being 80% as&nbsp;opposed to 70% full for the round trip.<\/p>\n<p>Having demonstrated consistence for an up peak analysis between the General Analysis and a traditional calculation methods, we will now consider a more complex traffic flow.<\/p>\n<h4>6.2&nbsp; Lunchtime peak at office block with roof top restaurant<\/h4>\n<p>Again a prestigious office block (with lower ground, ground and 6 upper floors), but this time the architect has suggested locating the office restaurant\/cafeteria on the top floor.&nbsp; The lifts are satisfactory to cope with the morning up peak, but will they cope with the lunchtime peak?<\/p>\n<p>In this case the lunchtime peak is likely to be made up of a combination of:<\/p>\n<ol>\n<li>passengers travelling from their offices to the roof top restaurant for lunch<\/li>\n<li>passengers travelling back to their offices after lunch at the restaurant<\/li>\n<li>passengers travelling to the ground floor to leave the building to buy sandwiches or eat out<\/li>\n<li>passengers returning from buying\/eating out<\/li>\n<\/ol>\n<p>The estimate of the combined traffic flows early during the lunch hour was as shown in figure 4 (less people are expected to travel within a five minute period than during the morning up peak).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/thetheoryandpracticeofgeneralanalysisliftcalculations\/fig%204%20summation%20lunchtime.bmp\" alt=\"\" width=\"506\" height=\"302\" border=\"0\"><\/p>\n<p><em>Figure 4&nbsp; Summation of lunchtime peak passenger flows for office block with restaurant on top floor<br><\/em><br>The analysis gives the following results:<\/p>\n<p>No of lifts&nbsp;&nbsp;&nbsp;&nbsp; 3<br>Contract Speed&nbsp;&nbsp;&nbsp;&nbsp; 2m\/s<br>Waiting Interval&nbsp;&nbsp;&nbsp;&nbsp; 34s<br>Capacity Factor (1250kg)&nbsp;&nbsp;&nbsp;&nbsp; 23%<br>Probable No of stops&nbsp;&nbsp;&nbsp;&nbsp; 8.6<br>Probable Lowest Reversal floor&nbsp;&nbsp;&nbsp;&nbsp; G<br>Probable Highest Reversal floor&nbsp;&nbsp;&nbsp;&nbsp; Restaurant<\/p>\n<p>The lifts always reach the top floor during their round trip, unlike during the up peak.&nbsp; Lifts are also stopping regularly during their journey down rather than expressing to the ground floor, another delay.<\/p>\n<p>In this case the lifts can cope with the specified traffic flow, but the service is poorer than during the morning up peak.<\/p>\n<h3>7.&nbsp; Current developments<\/h3>\n<p>The theory has been extended to incorporate double decker lifts and is currently being implemented within the Oasys LIFT program.&nbsp; The formulae will be published in due course.<\/p>\n<h3>8.&nbsp; Conclusions<\/h3>\n<p>The General Analysis gives us a tool to analyse any peak passenger traffic flow quickly and effectively.&nbsp; Analytical as opposed to the more comlex and computer power-hungry simulation models are likely to be our basic lift traffic analysis tools for the foreseeable future.&nbsp; The writer proposes this General Analysis method for implementation as a total solution for analysis of all peak passenger traffic flows.<\/p>\n<p>We need to define clearly expected passenger traffic before embarking on a detailed analysis, and interpret results remembering the limited accuracy of our input data.&nbsp; There appears to be little published data detailing surveys of lift passenger traffic flows &#8211; this needs to be addressed if we are to make full use of our new passenger traffic analysis tools.<\/p>\n<p>REFERENCES<\/p>\n<ol>\n<li>Peters R D CIBSE Building Srevices Engineerin gResearch and Technology Volume 11 Number 2 (1990)<\/li>\n<li>Barney G C and dos Santos S M Elevator Traffic Analysis Design and Control 2nd edn (London: Peter Peregrinus)(1985)<\/li>\n<\/ol>\n<h4>APPENDIX &#8211; General Analysis formulae<\/h4>\n<h5>A&nbsp;&nbsp;&nbsp; List of symbols&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<\/h5>\n<table class=\"art-article\" border=\"0\">\n<tbody>\n<tr>\n<td>\u00b5<em>i<\/em><\/td>\n<td>Passenger arrival rate at floor<em>&nbsp;i<\/em>&nbsp;(persons s<sup>-1<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<em>d<sub>ij<\/sub><\/em><\/td>\n<td>Probability of the destination floor of a call from&nbsp;<em>i<\/em>&nbsp;being the&nbsp;<em>j<\/em>th floor<\/td>\n<\/tr>\n<tr>\n<td><em>&nbsp;T<\/em><\/td>\n<td>Waiting interval (s)&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<em>N<\/em><\/td>\n<td>Number of floors<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<em>P<sub>ij<\/sub><sup>(n)<\/sup><\/em><\/td>\n<td>Probability of&nbsp;<em>n<\/em>&nbsp;passengers travelling from the&nbsp;<em>i<\/em>th to the&nbsp;<em>j<\/em>th floor in the time interval&nbsp;<em>T<\/em><\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<em>P<sub>ij<\/sub><\/em><\/td>\n<td>Probability of no calls from the<em>&nbsp;i<\/em>th to the<em>&nbsp;j<\/em>th floors in the time interval&nbsp;<em>T<\/em><\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<em>p<\/em>S<em><sub>1<\/sub><\/em><\/td>\n<td>Probability that a lift will stop at lowest floor&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<em>p<\/em>US<sub><em>2<\/em><\/sub>,&nbsp;<em>p<\/em>US<em><sub>3<\/sub><\/em>,&#8230;.<em>p<\/em>US<em><sub>N-1<\/sub><\/em><\/td>\n<td>Probability that the lift will stop at each of the intermediate floors on its journey up&nbsp;<\/td>\n<\/tr>\n<tr>\n<td><em>&nbsp;p<\/em>S<em><sub>N<\/sub><\/em><\/td>\n<td>Probability that the lift will stop at the hightest floor,&nbsp;<em>N<\/em>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td><em>&nbsp;pDS<sub>N-1<\/sub><\/em>,&#8230;<em>PDS<sub>2<\/sub><\/em><\/td>\n<td>Probability that the lift will stop at each of the intermediate floors on its&#8217; journey down&nbsp;<\/td>\n<\/tr>\n<tr>\n<td><em>&nbsp;S<\/em><\/td>\n<td>Probable number of stops&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<em>p<\/em>H<em><sub>n<\/sub><\/em><\/td>\n<td>Probability of nth floor being the highest reversal floor&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<em>p<\/em>L<em><sub>n<\/sub><\/em><\/td>\n<td>Probability of nth floor being the lowest reversal floor&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<em>H<\/em><\/td>\n<td>Highest reversal floor&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<em>L<\/em><\/td>\n<td>Lowest reversal floor&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;JWI<em>(i,j)<\/em><\/td>\n<td>Journey waiting interval for passengers travelling from the&nbsp;<em>i<\/em>th to the&nbsp;<em>j<\/em>th floor(s)<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;<em>T(n)<\/em><\/td>\n<td>Waiting interval, zone&nbsp;<em>n<\/em>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>&nbsp;SPLIT (Q<em>,i,j<\/em>)<\/td>\n<td>&nbsp;Proportion of passengers travelling from the&nbsp;<em>i<\/em>th to the<em>&nbsp;j<\/em>th floor who are using lifts in zone Q<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h5>B Call Probabilities<p><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image013.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;(1)&nbsp;&nbsp;&nbsp;<\/p><\/h5>\n<p><\/p>\n<p>Pij = exp(-\u00b5<em><sub>i&nbsp;<\/sub>Td<sub>ij<\/sub><\/em>)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2)<\/p>\n<h5>C&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Probable number of stops<\/h5>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image017.png\" alt=\"\" border=\"0\">&nbsp;(3)<\/p>\n<p>&nbsp;<img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image019.png\" alt=\"\" border=\"0\">&nbsp;(4)<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image021.png\" alt=\"\" border=\"0\">&nbsp;(5)<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image023.png\" alt=\"\" border=\"0\">&nbsp;(6)<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image027.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (7)<\/p>\n<h5>D&nbsp; Highest Reversal Floor<\/h5>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image029.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (8)&nbsp;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image031.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image033.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;(9)&nbsp;<\/p>\n<p>&nbsp;<img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image035.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (10)&nbsp;<\/p>\n<p>A good check for this is:&nbsp;&nbsp;&nbsp;&nbsp;<img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image037.png\" alt=\"\" border=\"0\"><\/p>\n<p>&nbsp;<img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image039.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(11)<\/p>\n<h5>E&nbsp; Lowest reversal floor<\/h5>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image041.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (12)&nbsp;<\/p>\n<p>&nbsp;<img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image043.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image045.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (13)&nbsp;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image047.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (14)&nbsp;<\/p>\n<p>&nbsp;<img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image049.png\" alt=\"\" border=\"0\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (15)&nbsp;<\/p>\n<h5>F Passengers in car calculation &#8211; eg ith floor journey up&nbsp;<\/h5>\n<p>&nbsp;<img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image051.png\" alt=\"\" border=\"0\">&nbsp; passengers enter the car<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image053.png\" alt=\"\" border=\"0\">leave the car&nbsp;<\/p>\n<p>G&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Overlapping Zones<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image059.png\" alt=\"\" border=\"0\">&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (16)&nbsp;<\/p>\n<p><\/p>\n<p>{Z} = {all zones serving both the<em>&nbsp;i<\/em>&nbsp;th and the&nbsp;<em>j<\/em>&nbsp;th floor}<\/p>\n<p><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/wordpress.peters-research.com\/images\/stories\/papers\/lifttrafficananlysisformulaeforthegeneralcasae\/image067.png\" alt=\"\" border=\"0\">&nbsp;&nbsp; (17)<\/p>\n<p><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The Theory and Practice of General Analysis Lift Calculations R D Peters BScOve Arup &amp; Partners This paper was presented at ELEVCON Amsterdam 1992, The International Congress on Vertical Transportation Technologies and first published in the IAEE book &#8220;Elevator Technology 4&#8221;, edited by G.C. Barney. It is reproduced with permission from The International Assocication of [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":860,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_canvas","meta":{"footnotes":""},"class_list":["post-1094","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The Theory and Practice of General Analysis Lift Calculations - Peters Research<\/title>\n<meta name=\"robots\" content=\"noindex, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Theory and Practice of General Analysis Lift Calculations - Peters Research\" \/>\n<meta property=\"og:description\" content=\"The Theory and Practice of General Analysis Lift Calculations R D Peters BScOve Arup &amp; Partners This paper was presented at ELEVCON Amsterdam 1992, The International Congress on Vertical Transportation Technologies and first published in the IAEE book &#8220;Elevator Technology 4&#8221;, edited by G.C. 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