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119 lines
3.8 KiB
C#
119 lines
3.8 KiB
C#
/*
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Copyright (c) 2023 Ahmed Kh. Zamil
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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using Esiur.Analysis.Statistics;
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using System;
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using System.Collections.Generic;
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using System.Text;
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using System.Text.RegularExpressions;
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namespace Esiur.Analysis.Queueing
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{
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public enum ProcessType
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{
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Markovian
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}
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public enum Discipline
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{
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}
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public class Queue
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{
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public ProcessType ArrivalProcess { get; set; }
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public ProcessType ServiceProcess { get; set; }
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public double ArrivalRate { get; set; }
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public double VisitRatio { get; set; } // for Mean Value Analysis
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public double ServiceRate { get; set; }
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public int Capacity { get; set; }
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public int Servers { get; set; }
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public int Population { get; set; }
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public string Label { get; set; }
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public double TrafficIntensity => Servers > 0 ? ArrivalRate / (Servers * ServiceRate) : ArrivalRate / ServiceRate;
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public double Pie(int n)
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{
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var rho = TrafficIntensity;
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// MM1
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if (Servers == 1 && Capacity == 0 && Population == 0)
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return Math.Pow(rho, n) * (1 - rho);
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// M/M/1/K
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if (Servers == 1 && Capacity == 1 && Population == 0)
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{
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if (rho == 1)
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return Math.Pow(rho, n) * (1 / (Servers + Capacity + 1));
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else
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return Math.Pow(rho, n) * ((1 - rho) / (1 - Math.Pow(rho, Servers + Capacity + 1)));
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}
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// M/M/Infinity
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if (Servers == 0 && Capacity == 0 && Population == 0)
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return (Math.Pow(rho, n) / n.Factorial()) * Math.Exp(-rho);
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// M/M/C
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if (Servers > 0 && Capacity > 0 && Population ==0)
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{
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double pie0 = 1;
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for (var i = 1; i < Capacity - 1; i++)
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pie0 += Math.Pow(Servers * rho, i) / i.Factorial();
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pie0 += Math.Pow(Servers * rho, Servers) / (Servers.Factorial() * (1 - rho));
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pie0 = 1 / pie0;
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return (Math.Pow(Servers * rho, n) / n.Factorial()) * pie0;
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}
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// M/M/C/K
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if (Servers > 0 && Capacity > 0 && Population > 0)
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{
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double pie0 = 1;
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for (var i = 1; i < Capacity - 1; i++)
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pie0 += Math.Pow(Servers * rho, i) / i.Factorial();
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double cc = Math.Pow(Servers, Servers) / Servers.Factorial();
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for(var i = Servers; i <= Servers + Capacity; i++)
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pie0 += cc * Math.Pow(rho, i);
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pie0 = 1 / pie0;
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return (Math.Pow(Servers * rho, n) / n.Factorial()) * pie0;
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}
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return 0;
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}
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}
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}
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