隊長與排隊長\ (1)隊長: 系統中的顧客數(n)期望值記為L s L_{s}Ls?；\ (2)排隊長: 系統中排隊等待服務的顧客數;\ 期望值記為L q L_{q}Lq?

逗留時間與等待時間\ (1)逗留時間：指一個顧客在系統中的全部停留時間；期望值，記為W s W_{\mathrm{s}}Ws?\ (2)等待時間:指一個顧客在系統中的排隊等待時間；期望值，記為W q W_{\mathrm{q}}Wq?\ W s W_{\mathrm{s}}Ws?=?W q W_{\mathrm{q}}Wq??+ E[服務時間]

其他相關指標\ (1)忙期: 指從顧客到達空閑服務機構起到服務機構再次空閑的時間長度；\ (2)忙期服務量：指一個忙期內系統平均完成服務的顧客數；\ (3)損失率: 指顧客到達排隊系統，未接受服務而離去的概率；\ (4)服務強度：ρ= λ/sμ；

``` function varargout = ChaoShiXiTong(varargin) guiSingleton = 1; guiState = struct('guiName', mfilename, ... 'guiSingleton', guiSingleton, ... 'guiOpeningFcn', @ChaoShiXiTongOpeningFcn, ... 'guiOutputFcn', @ChaoShiXiTongOutputFcn, ... 'guiLayoutFcn', [] , ... 'guiCallback', []); if nargin && ischar(varargin{1}) guiState.gui_Callback = str2func(varargin{1}); end

if nargout [varargout{1:nargout}] = guimainfcn(guiState, varargin{:}); else guimainfcn(guiState, varargin{:}); end % End initialization code - DO NOT EDIT

% --- Executes just before ChaoShiXiTong is made visible. function ChaoShiXiTong_OpeningFcn(hObject, eventdata, handles, varargin) % This function has no output args, see OutputFcn. % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % varargin command line arguments to ChaoShiXiTong (see VARARGIN)

% Choose default command line output for ChaoShiXiTong clc; handles.output = hObject;

% Update handles structure guidata(hObject, handles);

% UIWAIT makes ChaoShiXiTong wait for user response (see UIRESUME) % uiwait(handles.gaotiepaiduixitong);

% --- Outputs from this function are returned to the command line. function varargout = ChaoShiXiTong_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT); % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure varargout{1} = handles.output;

%-----------菜單部分的制作---------------------% %------------幫助菜單-------------------------%

function help_Callback(hObject, eventdata, handles)

% 菜單多服務臺系統仿真說明函數 function notice_Callback(hObject, eventdata, handles) h = figure('MenuBar','none','Name','多服務臺排隊論模型說明','NumberTitle',... 'off','units','pixels','position',[500,400,400,200],'Windowstyle','modal'); uicontrol('style','text','units','pixels','position',[50 60 300 80],... 'string','本仿真系統是標準的M/M/N排隊模型，各服務臺平均服務時間相同；服務員中間沒有休息、排隊容量不受限制；采用下次事件時間推進機制和先到先服務FIFO排隊規則；選擇選排隊最短的柜臺',... 'BackgroundColor',get(h,'Color'),... 'fontsize',16,'foregroundcolor','b','fontname','宋體'); uicontrol('string','關閉','units','pixels','position',[160 30 70 40],... 'fontsize',16,'fontweight','bold','foregroundcolor','b','callback',... 'delete(gcf);');

% 菜單運行指南 function guideCallback(hObject, eventdata, handles) h = figure('MenuBar','none','Name','運行指南','NumberTitle',... 'off','units','pixels','position',[500,400,400,200],'Windowstyle','modal'); uicontrol('style','text','units','pixels','position',[50 60 300 80],... 'string','輸入參數，點擊運行，可輸出模型結果',... 'BackgroundColor',get(h,'Color'),... 'fontsize',16,'foregroundcolor','r','fontname','黑體'); uicontrol('string','關閉','units','pixels','position',[160 30 70 40],... 'fontsize',16,'fontweight','bold','foregroundcolor','b','callback',... 'delete(gcf);'); % 退出菜單 function exitCallback(hObject, eventdata, handles) selection = questdlg(['關閉 ' get(handles.gaotiepaiduixitong,'Name') '?'],... ['關閉 ' get(handles.gaotiepaiduixitong,'Name') '...'],... ' 是 ',' 否 ',' 是 '); if strcmp(selection,' 否 ') return; end

% delete(handles.gaotiepaiduixitong) close(gcf);

%——————————————————————————————以下正文

%顧客平均等待時間編輯框 function wq_Callback(hObject, eventdata, handles)

function wq_CreateFcn(hObject, eventdata, handles) if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end

%服務員繁忙程度編輯框 function ps_Callback(hObject, eventdata, handles)

function ps_CreateFcn(hObject, eventdata, handles) if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end

%顧客平均排隊長度按鈕 function ls_Callback(hObject, eventdata, handles)

function ls_CreateFcn(hObject, eventdata, handles)

if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end

%設備配置彈出框 function fwts_Callback(hObject, eventdata, handles) global tai h = get(hObject,'value'); tai = h;

function fwts_CreateFcn(hObject, eventdata, handles) if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end

%顧客平均到達強度編輯框 function ddl_Callback(hObject, eventdata, handles)

function ddl_CreateFcn(hObject, eventdata, handles) if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end

%服務強度編輯框 function fwl_Callback(hObject, eventdata, handles)

function fwl_CreateFcn(hObject, eventdata, handles) if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end

% 運行按鈕 function calc_Callback(hObject, eventdata, handles) global Lambda %顧客到達強度 global Lamda %顧客購物強度 global Minu %柜臺服務強度 global tai %柜臺數

handles=guihandles; guidata(hObject,handles);%更新數據 %讀取到達強度，轉換為數字 lambda = str2double(get(handles.ddl,'string')); %讀取服務強度，轉換為數字 minu = str2double(get(handles.fwl,'string'));

%判斷仿真類型，服務臺個數為1時，即是單服務臺；大于1時，便是多服務臺 ru = lambda/(minutai); %服務機構的平均利用率 if (ru > 0)&&(ru < 1) &&(lambda>0) && (minu>0) && (tai>0) P0=0; %計算初始轉移概率 for i=0:tai-1 P0=P0+(rutai)^i/factorial(i); end P0=P0+((rutai)^tai)/(tai(1-ru)factorial(tai)); P0=1/P0; %初始轉移概率 Lq = ((tairu)^tai)ruP0/(factorial(tai)(1-ru)^2); %平均排隊長 Ls = Lq + lambda/minu; %平均隊長 Wq = Lq/lambda; %平均等待時間 Ps = 1-P0; %服務利用率 p=lambda/((minu)(tai)); %服務員繁忙程度 else errordlg('請仔細檢查，重新輸入','錯誤'); return; end %顯示顧客平均等待時間，顧客排隊長度，服務員繁忙程度 set(handles.wq,'string',num2str(Wq)); set(handles.ls,'string',num2str(Ls)); set(handles.ps,'string',num2str(p)); clear P0,clear Lq %刪除變量，釋放內存

% 重置按鈕 function reset_Callback(hObject, eventdata, handles) set(handles.ddl,'String',0); set(handles.fwl,'String',0);

set(handles.wq,'String','0'); set(handles.ls,'String','0'); set(handles.p,'String','0'); guidata(hObject, handles);

% --- Executes on button press in fangzhen. function fangzhen_Callback(hObject, eventdata, handles) global Lambda %顧客到達強度 global Lamda %顧客購物過強度 global Minu %服務員服務強度 global tai %柜臺數

load halton %% 生成隨機到達時間間隔、購物時間及每個柜臺結賬服務時間 Arrin = -1/Lambda.log(halton(1:1000,1)); %生成到達時間間隔 Carral = cumsum(Arrin); %到達時刻 Ncus = max(find(Carral<180)); %% 3個小時內到達的總顧客數 Shopping = -1/Lamda.log(halton(1:1000,2)); %生成購物時間間隔 Service = -1/Minu.*log(halton(1:1000,3)); %生成服務時間間隔 ArriGui = Carral+ Shopping; %所有顧客到達服務臺的到達時刻及順序，記為ArrGui

%% 初始化每個柜臺的狀態1 for g = 1:N Gui(g).Qu = [0,0]; % 按事件時間記錄柜臺g的排隊，0時刻排隊為0 Gui(g).Bu = [0,0];% 0表示空閑，1表示繁忙，0時刻空閑 Gui(g).Arrivaltime = []; %選擇柜臺g的顧客到達柜臺的時間 Gui(g).startser=[]; %選擇柜臺g的顧客開始接受服務的時間 Gui(g).wait=[]; %選擇柜臺g的顧客排隊等待的時間 Gui(g).servetime=[]; %選擇柜臺g的顧客接受服務的時間 Gui(g).Leavetime = []; %選擇柜臺g的顧客離開柜臺的時間 Gui(g).cusnu = []; % 選擇柜臺g的顧客代碼 Gui(g).staytime = []; %選擇柜臺g的顧客在服務臺停留的時間 end ```