#### 1, Experimental background

according to the time distribution of the first operation, the elevator simulation system is realized to test the time cost performance of students arriving at the first floor in different scenarios. Elevator system is a discrete system, which is driven by events. The state changes at discrete time points and operates in the mode of call first service.

#### 2, Known conditions

- Arrival time is the start time = wake-up time distribution + washing time distribution. The distribution of wake-up time is N ( 7.633 , 0.7822 ) N(7.633,0.7822) N(7.633,0.7822), the distribution of washing time is N ( 0.17689 , 0.00235 ) N(0.17689,0.00235) N(0.17689,0.00235) .
- The running speed of the elevator is 1.58s/floor.
- Residence time of each floor U ( 10 , 60 ) U(10,60) U(10,60) seconds.
- Elevator operation strategy: call first, service first + operation direction floor sequencing strategy

#### 3, Implementation process

the elevator has three states: idle, running under full load (number of people < 10), running and full load (number of people = 10). Set Event_queue is the sequence of events. The first behavior is the start time and consumption time. The second behavior is the current state. 1 is arrival, 0 is in the elevator, and - 1 determines whether to reach the first floor or out of the elevator. Let queue be the waiting sequence, and each line represents missing multiplication. The first digit is the number of people, and the second digit and later are the ID number

Set queue_ in_ The ID that the elevator records in the elevator.

There are three situations for elevator operation:

- Students arrive to call the elevator ① yes and open door ③ whether it is full ② whether it is on the first floor.
- When the elevator is running, arrive at the call floor, judge whether there is a queue below the call floor in turn, and if so, join the elevator queue when the elevator is running downward under the condition that the elevator is not full.
- The elevator closes and waits for a call.

Case 1 type=1

Figure 1 student arrival flow chartCase 2 type=0

Figure 2 flow chart of elevator movement processCase 3 type = -1

Fig. 3 flow chart of elevator door closing waiting process#### 4, Effect test

Operation process:

......

Scene group comparison

① There are 20 students on each floor

Number of floors | 5 | 6 | 7 | 8 | 9 | |

Total number | 100 | 120 | 140 | 160 | 180 | |

Average consumption time | 1 | 43.511s | 41.365 | 67.589 | 52.908 | 65.652 |

2 | 44.179s | 48.702 | 53.102 | 61.904 | 86.502 | |

3 | 41.515 | 53.731 | 60.289 | 59.374 | 64.415 | |

4 | 41.056 | 49.858 | 60.929 | 53.575 | 71.541 | |

5 | 38.552 | 67.702 | 40.739 | 64.393 | 74.349 | |

Total average | 41.762 | 52.271 | 56.5296 | 58.4308 | 72.4918 |

Figure 5 Comparison of average consumption time of different floors

② According to the actual data of the author's dormitory building, the average service time of 64 people on each floor is 261.192s

Table 2 average consumption schedule of 64 people on the 9th floor

1 | 2 | 3 | 4 | 5 | average |

376.576 | 196.350 | 267.617 | 266.110 | 199.309 | 261.192s |

#### 5, Conclusion

Compared with the average time performance, the average time cost increases with the increase of the number of floors and the total number of people.

#### Appendix:

Main.m

clc;clear; close all; %*********************** Event_queue= [];%Event queue N=6;%Number of floors student_num = 20*N; queue = zeros(N,20); elevator_loc = 1;%Elevator floor elevator_num_threshold = 10;%Maximum number of elevators num_in_elevator = 0;%Number of people in the elevator time_every_floor = 0.0004388; %2.1361/3600s elevator_dst = 0; queue_in_elevator = []; elevator_door = 0;%Status of elevator door wakeup_time=normrnd(7.633,0.7822,1,student_num); wash_time=normrnd(0.17689,0.00235,1,student_num); t=wakeup_time+wash_time; time=sort(t); for t=1:student_num s(t)=student; s(t).id = t; s(t).StartTime = time(t); s(t).floor = unidrnd(N); %floor=1 2 3 4 5 6 7 8 9 s(t).left_elevator = 0;%Time to leave the elevator if s(t).floor == 1 s(t).left_elevator = s(t).StartTime; else Event_queue = insert_Event_queue(Event_queue, s(t).StartTime, 1,s(t).id); end end t_floor = []; %Print and generate the corresponding floor of students for i = 1:student_num t_floor = [t_floor s(i).floor]; end t_floor; t_start=[]; %Print and generate the corresponding start time of students entering the elevator system for i =1:student_num t_start = [t_start s(i).StartTime]; end t_start; t=0; mid = 0; while(~isempty(Event_queue)) [t,type,id,Event_queue]=pop_Event_queue(Event_queue); %********************************************************************************************** if type == -1 %Elevator door closing elevator_door = 0; if elevator_loc == 1 for i = N:-1:1 if queue(i,1) ~= 0 elevator_dst = i; break; end end if i == 1 elevator_dst = 0; else Event_queue = insert_Event_queue(Event_queue,t+time_every_floor*(elevator_dst-1), 0, elevator_dst); end else time_arrive_next_floor = t + time_every_floor;%Go to the next floor Event_queue = insert_Event_queue(Event_queue,time_arrive_next_floor, 0, elevator_loc-1);%insert change event end %********************************************************************************************** elseif type == 0 %Elevator operation elevator_loc = id;%Elevator floor elevator_door = 1; if elevator_loc == 1%Get out of the elevator while(num_in_elevator ~= 0) temp_id = queue_in_elevator(1); s(temp_id).left_elevator = t;%Record the time queue_in_elevator = queue_in_elevator(2:length(queue_in_elevator)); num_in_elevator = num_in_elevator - 1; end % queue_in_elevator = []; elevator_dst = 0; time_elevator_close = t + (10 + 50 * rand())/3600; Event_queue = insert_Event_queue(Event_queue,time_elevator_close, -1, elevator_loc);%insert close event elseif elevator_loc == elevator_dst elevator_dst = 1; time_elevator_close = t + (10 + 50 * rand())/3600; Event_queue = insert_Event_queue(Event_queue,time_elevator_close, -1, elevator_loc);%insert close event if queue(elevator_loc,1) ~= 0 [queue, pop_id] = pop_queue(queue,elevator_loc,elevator_num_threshold-num_in_elevator); while(~isempty(pop_id)) temp_id = pop_id(1); queue_in_elevator = [queue_in_elevator temp_id];%ID Put it in the elevator num_in_elevator = num_in_elevator + 1; pop_id = pop_id(2:length(pop_id)); end end elseif elevator_dst == 1 if queue(elevator_loc,1) ~= 0 && num_in_elevator < elevator_num_threshold%Determine whether someone [queue, pop_id] = pop_queue(queue,elevator_loc,elevator_num_threshold-num_in_elevator); while(~isempty(pop_id))%Layer by layer judgment temp_id = pop_id(1); queue_in_elevator = [queue_in_elevator temp_id]; num_in_elevator = num_in_elevator + 1; pop_id = pop_id(2:length(pop_id)); end time_elevator_close = t + (10 + 50 * rand())/3600; Event_queue = insert_Event_queue(Event_queue,time_elevator_close, -1, elevator_loc);%insert close event else Event_queue = insert_Event_queue(Event_queue,t+time_every_floor, 0, elevator_loc-1);%insert change event end end %********************************************************************************************** elseif type == 1% Elevator. if elevator_loc == s(id).floor && elevator_door == 1%The elevator is just in and the door is open queue_in_elevator = [queue_in_elevator id]; num_in_elevator = num_in_elevator + 1; elseif queue(s(id).floor,1) == 0 %Judge whether the current floor queue is empty temp_num_in_queue = queue(s(id).floor,1);%Number of people on this floor queue(s(id).floor,temp_num_in_queue+2) = id; queue(s(id).floor,1) = queue(s(id).floor,1) + 1; if elevator_loc == 1 && elevator_dst == 0 %At first, the elevator was on the first floor for i = N:-1:1 if queue(i,1) ~= 0 elevator_dst = i; break; end end Event_queue = insert_Event_queue(Event_queue,t+time_every_floor*(elevator_dst-1), 0, elevator_dst);%hold id Changed to the floor end else %else, join the queue temp_num_in_queue = queue(s(id).floor,1); queue(s(id).floor,temp_num_in_queue+2) = id; queue(s(id).floor,1) = queue(s(id).floor,1) + 1; end end end % Graphical visualization of results t_cost=[]; t_left=[]; for i =1:student_num t_cost = [t_cost (s(i).left_elevator-s(i).StartTime)*3600]; end for i =1:student_num t_left = [t_left s(i).left_elevator]; end x=(1:student_num); figure plot(x,t_cost,'LineWidth',1.5); xlabel('ID'); ylabel('Time consuming(Unit: Second)'); grid on; %Result value output fprintf('Number of floors: %d Total number of students:%d\n',N,student_num); fprintf('-----------------------------------------------------------\n') t_start_hour=floor(t_start); t_start_middle = (t_start-floor(t_start))*60; t_start_min=floor(t_start_middle); t_start_second=(t_start_middle-floor(t_start_middle))*60; t_left_hour=floor(t_left); t_left_middle = (t_left-floor(t_left))*60; t_left_min=floor(t_left_middle); t_left_second=(t_left_middle-floor(t_left_middle))*60; for k=1:student_num fprintf('ID be entitled as %d My students are in the second grade %d The departure time on the first floor is %d:%d:%0.1f,Departure time is %d:%d:%0.1f,time consuming%0.1fs\n',s(k).id,s(k).floor,t_start_hour(k),t_start_min(k),t_start_second(k),t_left_hour(k),t_left_min(k),t_left_second(k),t_cost(k)); end fprintf('-----------------------------------------------------------\n') fprintf('The average length of time students spend taking the elevator= %f second\n',mean(t_cost));

pop_queuw.m

function [ queue, pop_id ] = pop_queue( queue, index ,num_to_pop ) pop_id = []; num_pop = 0; if queue(index,1) <= num_to_pop %The number of students who want to withdraw is less than the number of queuing on the current floor num_pop = queue(index,1); %Everyone in line took it out for i = 2:(num_pop+1) pop_id = [pop_id queue(index,i)]; if queue(index,i) == 0 bb = 1; end end queue(index,:) = 0; else %The number of students you want to withdraw is more than the number of people in the queue on the current floor num_pop = num_to_pop; queue(index,1) = queue(index,1) - num_pop; for i = 2:(num_pop +1) pop_id = [pop_id queue(index,i)]; if queue(index,i) == 0 bb = 1; end queue(index,i) = 0; %Dispose of the removed student position 0 end for i = 2:(queue(index,1)+1) queue(index,i) = queue(index,i+num_pop); %Line up the students who are not taken out from the back and move forward queue(index,i+num_pop) = 0; %The student position moved forward is disposed of 0 end end end

insert_Event_queue.m

function event_queue=insert_Event_queue(event_queue,time, type,id) if isempty(event_queue) event_queue = [time type id]'; else s = size(event_queue); %check the start and end if event_queue(1,1) >= time %add to the start event_queue = [[time type id]' event_queue(:,1:s(2))]; elseif event_queue(1,s(2)) <= time %add to the end event_queue = [event_queue(:,1:s(2)) [time type id]']; else for n = 1:s(2) %go through the event queue and find the right place to insert if event_queue(1,n)<time %insert the time and type event_queue = [event_queue(:,1:n) [time type id]' event_queue(:,n+1:s(2))]; break; end end end end

pop_Event_queue.m

function [time, type, id, event_queue]=pop_Event_queue(event_queue) time= event_queue(1,1);% move the timer type = event_queue(2,1); id = event_queue(3,1); s = size(event_queue); if s == [3 1]% only one event existed event_queue = []; else %more than one event existed %push the fisrt event out. event_queue=event_queue(:,2:s(2));%Remove the previous one end

reference resources

[1]. Liuss Shengsheng cabin