mms_function.m

这是一个基于M/M/S类型的排队论仿真程序。M/M/S表示到达时间为负指数分布

function[block_rate,use_rate]=MMS_function(mean_arr,mean_serv,peo_num,server_num)
state=zeros(3,peo_num);  
                %用一个三行矩阵表示每个顾客的状态
                %三行依次为：到达时间间隔，服务时间，等待时间
state(1,:)=exprnd(mean_arr,1,peo_num);
                %各顾客到达时间间隔服从负指数分布
state(2,:)=exprnd(mean_serv,1,peo_num);
for i=1:server_num
    state(3,1:server_num)=0;
end
arr_time=cumsum(state(1,:));
                %生成各顾客到达时间的行矩阵
state(1,:)=arr_time;
lea_time(1:server_num)=sum(state(:,1:server_num));
                %先计算前N名顾客的离开时间
serv_desk=lea_time(1:server_num);
                %构造一个N元行向量，记录正在被服务的顾客的离开时间
for i=(server_num+1):peo_num
   if arr_time(i)>min(serv_desk)
       state(3,i)=0;                    
   else 
       state(3,i)=min(serv_desk)-arr_time(i);
                %第i个顾客到达，服务台满，等待时间为
                %当时服务台最早离开的顾客的离开时间减去第i个顾客的到达时间
   end
   lea_time(i)=sum(state(:,i));
   for j=1:server_num 
           if serv_desk(j)==min(serv_desk)
               serv_desk(j)=lea_time(i);
               break
           end
                %更新服务台，便于时间比较              
   end
end

max_time=lea_time(peo_num)*2;
%max_time用于占据服务台的空位，便于时间比较
%初始化
serv_desk(1:server_num)=max_time;
block_num=0;
block_line=0;
for i=1:peo_num
    if block_line==0
        find_max=0;    
        for j=1:server_num
            if serv_desk(j)==max_time
                find_max=1;    %服务台有空位
                break
            else continue
            end
        end
        if find_max==1
            %更新服务台
            serv_desk(j)=lea_time(i);
            for k=1:server_num
                if serv_desk(k)<arr_time(i)
                    serv_desk(k)=max_time;
                else continue
                end
            end
        else
            if arr_time(i)>min(serv_desk)
                %时间间隔T内有人离开
                for k=1:server_num
                    if arr_time(i)>serv_desk(k)
                        serv_desk(k)=lea_time(i);
                        break
                    else continue
                    end
                end
                for k=1:server_num
                    if arr_time(i)>serv_desk(k)
                        serv_desk(k)=max_time;
                    else continue
                    end
                end
            else   %时间间隔T内有人离开
                block_num=block_num+1;
                block_line=block_line+1;
            end
        end
    else    %队长不为0的情况
        n=0;
        %计算时间间隔T内离开的人数n
        for k=1:server_num
            if arr_time(i)>serv_desk(k)
                n=n+1;
                serv_desk(k)=max_time;
            else continue
            end
        end
        for k=1:block_line
            if arr_time(i)>lea_time(i-k)
                n=n+1;
            else continue
            end
        end
        if n<block_line+1
           % n<block_line+1说明队列依然存在阻塞
            block_num=block_num+1;
            for k=0:n-1
                if lea_time(i-block_line+k)>arr_time(i)
                    for m=1:server_num
                        if serv_desk(m)==max_time
                            serv_desk(m)=lea_time(i-block_line+k)
                            break
                        else continue
                        end
                    end
                else
                    continue
                end
            end
            block_line=block_line-n+1;
        else    % n>=block_line+1说明队列不存在阻塞
                %更新服务台时间表及队列长度
            for k=0:block_line
                if arr_time(i)<lea_time(i-k)
                    for m=1:server_num
                        if serv_desk(m)==max_time
                            serv_desk(m)=lea_time(i-k)
                            break
                        else continue
                        end
                    end
                else
                    continue
                end
            end
            block_line=0;
        end
    end
end
                                                   
block_rate=block_num/peo_num;
%资源利用率＝peo_num/服务台不停工作所能服务的最大顾客数
use_rate=peo_num/(lea_time(peo_num)*(server_num/mean_serv));