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Tema: Modelarea sistemelor de aşteptare cu distribuţii tip PH. Scopul lucrării: Studierea metodelor de descriere şi de evaluare a sistemelor de aşteptare prioritare. Consideraţii teoretice: Formarea şirurilor de aşteptare şi servirea cererilor în sistemul de aşteptare de regulă se face după disciplina de servire FIFO. În unele cazuri, este nevoie de a asigura o altă disciplină de formare a SA în dependenţă de urgenţa cererii, avînd o astfel de prioritate de servire. În continuare vom presupune că în SA prioritatea cererii creşte o dată cu micşorarea indicelui clasei la care aparţine. Dacă i<j, cererile ce prioritatea i vor avea prioritate mai înaltă decît cele cu prioritatea j. Modelele cu prioritate se impart în modele ale SA: M/M/1 cu prioritate relativă şi cu prioritate absolută. Servirea cererilor conform priorităţii relative presupune manifestarea priorirăţii numai în momentul eliberării serverului şi a selectării, care va fi definită din SA, adică va fi deservită cererea care are cea mai mare prioritate. Date iniţiale: Parametrii SA: λ 1 =0.79; λ 2 =33; λ 3 =111; λ 4 =7.01; λ 5 =4.95; λ 6 =148; λ 7 =1;

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Tema: Modelarea sistemelor de ateptare cu distribuii tip PH. Scopul lucrrii: Studierea metodelor de descriere i de evaluare a sistemelor de ateptare prioritare.Consideraii teoretice: Formarea irurilor de ateptare i servirea cererilor n sistemul de ateptare de regul se face dup disciplina de servire FIFO. n unele cazuri, este nevoie de a asigura o alt disciplin de formare a SA n dependen de urgena cererii, avnd o astfel de prioritate de servire. n continuare vom presupune c n SA prioritatea cererii crete o dat cu micorarea indicelui clasei la care aparine. Dac iM1;\\1;M1 = [16,0,1,0,0,0,0] [t1>M2;t3,t4>M4;t3,t5,t7>M0;\\1;0.968173138128581;0.0318268618714195;M2 = [15,1,1,0,0,0,0] [t1>M3;t3,t4>M6;t3,t5,t7,t2>M1;\\1;0.968173138128581;0.0318268618714195;M3 = [14,2,1,0,0,0,0] [t1>M5;t3,t4>M8;t3,t5,t7,t2>M2;\\1;0.968173138128581;0.0318268618714195;M4 = [16,0,0,0,1,0,0] [t1>M6;t6,t7>M0;\\1;1;M5 = [13,3,1,0,0,0,0] [t1>M7;t3,t4>M10;t3,t5,t7,t2>M3;\\1;0.968173138128581;0.0318268618714195;M6 = [15,1,0,0,1,0,0] [t1>M8;t6,t7,t2>M1;\\1;1;M7 = [12,4,1,0,0,0,0] [t1>M9;t3,t4>M12;t3,t5,t7,t2>M5;\\1;0.968173138128581;0.0318268618714195;M8 = [14,2,0,0,1,0,0] [t1>M10;t6,t7,t2>M2;\\1;1;M9= [11,5,1,0,0,0,0] [t1>M11;t3,t4>M14;t3,t5,t7,t2>M7;\\1;0.968173138128581;0.0318268618714195;M10 = [13,3,0,0,1,0,0] [t1>M12;t6,t7,t2>M3;\\1;1;M11=[10,6,1,0,0,0,0][t1>M13;t3,t4>M16;t3,t5,t7,t2>M9;\\1;0.968173138128581;0.0318268618714195;M12 = [12,4,0,0,1,0,0] [t1>M14;t6,t7,t2>M5;\\1;1;M13=[9,7,1,0,0,0,0][t1>M15;t3,t4>M18;t3,t5,t7,t2>M11;\\1;0.968173138128581;0.0318268618714195;M14 = [11,5,0,0,1,0,0] [t1>M16;t6,t7,t2>M7;\\1;1;M15=[8,8,1,0,0,0,0][t1>M17;t3,t4>M20;t3,t5,t7,t2>M13;\\1;0.968173138128581;0.0318268618714195;M16 = [10,6,0,0,1,0,0] [t1>M18;t6,t7,t2>M9;\\1;1;M17=[7,9,1,0,0,0,0][t1>M19;t3,t4>M22;t3,t5,t7,t2>M15;\\1;0.968173138128581;0.0318268618714195;M18 = [9,7,0,0,1,0,0] [t1>M20;t6,t7,t2>M11;\\1;1;M19=[6,10,1,0,0,0,0][t1>M21;t3,t4>M24;t3,t5,t7,t2>M17;\\1;0.968173138128581;0.0318268618714195;M20 = [8,8,0,0,1,0,0][t1>M22;t6,t7,t2>M13;\\1;1;M21=[5,11,1,0,0,0,0][t1>M23;t3,t4>M26;t3,t5,t7,t2>M19;\\1;0.968173138128581;0.0318268618714195;M22 = [7,9,0,0,1,0,0] [t1>M24;t6,t7,t2>M15;\\1;1;M23=[4,12,1,0,0,0,0][t1>M25;t3,t4>M28;t3,t5,t7,t2>M21;\\1;0.968173138128581;0.0318268618714195;M24 = [6,10,0,0,1,0,0] [t1>M26;t6,t7,t2>M17;\\1;1;M25=[3,13,1,0,0,0,0][t1>M27;t3,t4>M30;t3,t5,t7,t2>M23;\\1;0.968173138128581;0.0318268618714195;M26 = [5,11,0,0,1,0,0] [t1>M28;t6,t7,t2>M19;\\1;1;M27=[2,14,1,0,0,0,0] [t1>M29;t3,t4>M32;t3,t5,t7,t2>M25;\\1;0.968173138128581;0.0318268618714195;M28 = [4,12,0,0,1,0,0] [t1>M30;t6,t7,t2>M21;\\1;1;M29=[1,15,1,0,0,0,0][t1>M31;t3,t4>M33;t3,t5,t7,t2>M27;\\1;0.968173138128581;0.0318268618714195;M30 = [3,13,0,0,1,0,0] [t1>M32;t6,t7,t2>M23;\\1;1;M31 = [0,16,1,0,0,0,0] [t3,t4>M34;t3,t5,t7,t2>M29;\\0.968173138128581;0.0318268618714195;M32 = [2,14,0,0,1,0,0] [t1>M33;t6,t7,t2>M25;\\1;1;M33 = [1,15,0,0,1,0,0] [t1>M34;t6,t7,t2>M27;\\1;1;M34 = [0,16,0,0,1,0,0] [t6,t7,t2>M29;\\1;

Caracteristicele de performan:

2D3D

P1

P5

P6

P7

Schema 2 SA: M/H2/2/n/N (FIFO, block)Pentru P1, P5, P6, P7

Totally found markings number = 35PositionsList: p1;p2;p3;p4;p5;p6;p7;M0 = [17,0,0,0,0,0,1] [t1,t2,t5>M1;t1,t2,t4>M2;\\0.5;0.5;M1 = [16,0,0,0,1,0,0] [t1>M3;t6,t7>M0;\\1;1;M2 = [16,0,1,0,0,0,0] [t1>M4;t3,t7>M0;\\1;1;M3 = [15,1,0,0,1,0,0] [t1>M5;t6,t7,t2,t5>M1;t6,t7,t2,t4>M2;\\1;0.5;0.5;M4 = [15,1,1,0,0,0,0] [t1>M6;t3,t7,t2,t5>M1;t3,t7,t2,t4>M2;\\1;0.5;0.5;M5 = [14,2,0,0,1,0,0] [t1>M7;t6,t7,t2,t5>M3;t6,t7,t2,t4>M4;\\1;0.5;0.5;M6 = [14,2,1,0,0,0,0] [t1>M8;t3,t7,t2,t5>M3;t3,t7,t2,t4>M4;\\1;0.5;0.5;M7 = [13,3,0,0,1,0,0] [t1>M9;t6,t7,t2,t5>M5;t6,t7,t2,t4>M6;\\1;0.5;0.5;M8 = [13,3,1,0,0,0,0] [t1>M10;t3,t7,t2,t5>M5;t3,t7,t2,t4>M6;\\1;0.5;0.5;M9 = [12,4,0,0,1,0,0] [t1>M11;t6,t7,t2,t5>M7;t6,t7,t2,t4>M8;\\1;0.5;0.5;M10 = [12,4,1,0,0,0,0] [t1>M12;t3,t7,t2,t5>M7;t3,t7,t2,t4>M8;\\1;0.5;0.5;M11 = [11,5,0,0,1,0,0] [t1>M13;t6,t7,t2,t5>M9;t6,t7,t2,t4>M10;\\1;0.5;0.5;M12 = [11,5,1,0,0,0,0] [t1>M14;t3,t7,t2,t5>M9;t3,t7,t2,t4>M10;\\1;0.5;0.5;M13 = [10,6,0,0,1,0,0] [t1>M15;t6,t7,t2,t5>M11;t6,t7,t2,t4>M12;\\1;0.5;0.5;M14 = [10,6,1,0,0,0,0] [t1>M16;t3,t7,t2,t5>M11;t3,t7,t2,t4>M12;\\1;0.5;0.5;M15 = [9,7,0,0,1,0,0] [t1>M17;t6,t7,t2,t5>M13;t6,t7,t2,t4>M14;\\1;0.5;0.5;M16 = [9,7,1,0,0,0,0] [t1>M18;t3,t7,t2,t5>M13;t3,t7,t2,t4>M14;\\1;0.5;0.5;M17 = [8,8,0,0,1,0,0] [t1>M19;t6,t7,t2,t5>M15;t6,t7,t2,t4>M16;\\1;0.5;0.5;M18 = [8,8,1,0,0,0,0] [t1>M20;t3,t7,t2,t5>M15;t3,t7,t2,t4>M16;\\1;0.5;0.5;M19 = [7,9,0,0,1,0,0] [t1>M21;t6,t7,t2,t5>M17;t6,t7,t2,t4>M18;\\1;0.5;0.5;M20 = [7,9,1,0,0,0,0] [t1>M22;t3,t7,t2,t5>M17;t3,t7,t2,t4>M18;\\1;0.5;0.5;M21 = [6,10,0,0,1,0,0] [t1>M23;t6,t7,t2,t5>M19;t6,t7,t2,t4>M20;\\1;0.5;0.5;M22 = [6,10,1,0,0,0,0] [t1>M24;t3,t7,t2,t5>M19;t3,t7,t2,t4>M20;\\1;0.5;0.5;M23 = [5,11,0,0,1,0,0] [t1>M25;t6,t7,t2,t5>M21;t6,t7,t2,t4>M22;\\1;0.5;0.5;M24 = [5,11,1,0,0,0,0] [t1>M26;t3,t7,t2,t5>M21;t3,t7,t2,t4>M22;\\1;0.5;0.5;M25 = [4,12,0,0,1,0,0] [t1>M27;t6,t7,t2,t5>M23;t6,t7,t2,t4>M24;\\1;0.5;0.5;M26 = [4,12,1,0,0,0,0] [t1>M28;t3,t7,t2,t5>M23;t3,t7,t2,t4>M24;\\1;0.5;0.5;M27 = [3,13,0,0,1,0,0] [t1>M29;t6,t7,t2,t5>M25;t6,t7,t2,t4>M26;\\1;0.5;0.5;M28 = [3,13,1,0,0,0,0] [t1>M30;t3,t7,t2,t5>M25;t3,t7,t2,t4>M26;\\1;0.5;0.5;M29 = [2,14,0,0,1,0,0] [t1>M31;t6,t7,t2,t5>M27;t6,t7,t2,t4>M28;\\1;0.5;0.5;M30 = [2,14,1,0,0,0,0] [t1>M32;t3,t7,t2,t5>M27;t3,t7,t2,t4>M28;\\1;0.5;0.5;M31 = [1,15,0,0,1,0,0] [t1>M33;t6,t7,t2,t5>M29;t6,t7,t2,t4>M30;\\1;0.5;0.5;M32 = [1,15,1,0,0,0,0] [t1>M34;t3,t7,t2,t5>M29;t3,t7,t2,t4>M30;\\1;0.5;0.5;M33 = [0,16,0,0,1,0,0] [t6,t7,t2,t5>M31;t6,t7,t2,t4>M32;\\0.5;0.5;M34 = [0,16,1,0,0,0,0] [t3,t7,t2,t5>M31;t3,t7,t2,t4>M32;\\0.5;0.5;

Caracteristicele de performan:

2D3D

P1

P5

P6

P7

Schema 3 SA: M/Er/n/N (FIFO, block)Pentru P1, P3, P5, P7

Totally found markings number = 52PositionsList: p1;p2;p3;p4;p5;p7;M0 = [17,0,0,0,0,1] [t1,t5>M1;\\1;M1 = [16,0,1,0,0,0] [t1>M2;t2>M3;\\1;1;M2 = [15,1,1,0,0,0] [t1>M4;t2>M5;\\1;1;M3 = [16,0,0,1,0,0] [t1>M5;t3>M6;\\1;1;M4 = [14,2,1,0,0,0] [t1>M7;t2>M8;\\1;1;M5 = [15,1,0,1,0,0] [t1>M8;t3>M9;\\1;1;M6 = [16,0,0,0,1,0] [t1>M9;t4>M0;\\1;1;M7 = [13,3,1,0,0,0] [t1>M10;t2>M11;\\1;1;M8 = [14,2,0,1,0,0] [t1>M11;t3>M12;\\1;1;M9 = [15,1,0,0,1,0] [t1>M12;t4,t5>M1;\\1;1;M10 = [12,4,1,0,0,0] [t1>M13;t2>M14;\\1;1;M11 = [13,3,0,1,0,0] [t1>M14;t3>M15;\\1;1;M12 = [14,2,0,0,1,0] [t1>M15;t4,t5>M2;\\1;1;M13 = [11,5,1,0,0,0] [t1>M16;t2>M17;\\1;1;M14 = [12,4,0,1,0,0] [t1>M17;t3>M18;\\1;1;M15 = [13,3,0,0,1,0] [t1>M18;t4,t5>M4;\\1;1;M16 = [10,6,1,0,0,0] [t1>M19;t2>M20;\\1;1;M17 = [11,5,0,1,0,0] [t1>M20;t3>M21;\\1;1;M18 = [12,4,0,0,1,0] [t1>M21;t4,t5>M7;\\1;1;M19 = [9,7,1,0,0,0] [t1>M22;t2>M23;\\1;1;M20 = [10,6,0,1,0,0] [t1>M23;t3>M24;\\1;1;M21 = [11,5,0,0,1,0] [t1>M24;t4,t5>M10;\\1;1;M22 = [8,8,1,0,0,0] [t1>M25;t2>M26;\\1;1;M23 = [9,7,0,1,0,0] [t1>M26;t3>M27;\\1;1;M24 = [10,6,0,0,1,0] [t1>M27;t4,t5>M13;\\1;1;M25 = [7,9,1,0,0,0] [t1>M28;t2>M29;\\1;1;M26 = [8,8,0,1,0,0] [t1>M29;t3>M30;\\1;1;M27 = [9,7,0,0,1,0] [t1>M30;t4,t5>M16;\\1;1;M28 = [6,10,1,0,0,0] [t1>M31;t2>M32;\\1;1;M29 = [7,9,0,1,0,0] [t1>M32;t3>M33;\\1;1;M30 = [8,8,0,0,1,0] [t1>M33;t4,t5>M19;\\1;1;M31 = [5,11,1,0,0,0] [t1>M34;t2>M35;\\1;1;M32 = [6,10,0,1,0,0] [t1>M35;t3>M36;\\1;1;M33 = [7,9,0,0,1,0] [t1>M36;t4,t5>M22;\\1;1;M34 = [4,12,1,0,0,0] [t1>M37;t2>M38;\\1;1;M35 = [5,11,0,1,0,0] [t1>M38;t3>M39;\\1;1;M36 = [6,10,0,0,1,0] [t1>M39;t4,t5>M25;\\1;1;M37 = [3,13,1,0,0,0] [t1>M40;t2>M41;\\1;1;M38 = [4,12,0,1,0,0] [t1>M41;t3>M42;\\1;1;M39 = [5,11,0,0,1,0] [t1>M42;t4,t5>M28;\\1;1;M40 = [2,14,1,0,0,0] [t1>M43;t2>M44;\\1;1;M41 = [3,13,0,1,0,0] [t1>M44;t3>M45;\\1;1;M42 = [4,12,0,0,1,0] [t1>M45;t4,t5>M31;\\1;1;M43 = [1,15,1,0,0,0] [t1>M46;t2>M47;\\1;1;M44 = [2,14,0,1,0,0] [t1>M47;t3>M48;\\1;1;M45 = [3,13,0,0,1,0] [t1>M48;t4,t5>M34;\\1;1;M46 = [0,16,1,0,0,0] [t2>M49;\\1;M47 = [1,15,0,1,0,0] [t1>M49;t3>M50;\\1;1;M48 = [2,14,0,0,1,0] [t1>M50;t4,t5>M37;\\1;1;M49 = [0,16,0,1,0,0] [t3>M51;\\1;M50 = [1,15,0,0,1,0] [t1>M51;t4,t5>M40;\\1;1;M51 = [0,16,0,0,1,0] [t4,t5>M43;\\1;

Caracteristicele de performan:

2D3D

P1

P3

P5

P7

Schema 4 SA: M/Er/1/n/N (FIFO, block)Pentru P1, P3, P5, P8, P6

Totally found markings number = 52PositionsList: p1;p2;p3;p4;p5;p6;p7;p8;M0 = [17,0,0,0,0,0,1,0] [t1,t2>M1;\\1;M1 = [16,0,1,0,0,0,0,0] [t1>M2;t3,t4>M4;t3,t5,t7>M0;\\1;0.5;0.5;M2 = [15,1,1,0,0,0,0,0] [t1>M3;t3,t4>M6;t3,t5,t7,t2>M1;\\1;0.5;0.5;M3 = [14,2,1,0,0,0,0,0] [t1>M5;t3,t4>M9;t3,t5,t7,t2>M2;\\1;0.5;0.5;M4 = [16,0,0,0,1,0,0,0] [t1>M6;t6>M7;\\1;1;M5 = [13,3,1,0,0,0,0,0] [t1>M8;t3,t4>M12;t3,t5,t7,t2>M3;\\1;0.5;0.5;M6 = [15,1,0,0,1,0,0,0] [t1>M9;t6>M10;\\1;1;M7 = [16,0,0,0,0,0,0,1] [t1>M10;t8,t7>M0;\\1;1;M8 = [12,4,1,0,0,0,0,0] [t1>M11;t3,t4>M15;t3,t5,t7,t2>M5;\\1;0.5;0.5;M9 = [14,2,0,0,1,0,0,0] [t1>M12;t6>M13;\\1;1;M10 = [15,1,0,0,0,0,0,1] [t1>M13;t8,t7,t2>M1;\\1;1;M11 = [11,5,1,0,0,0,0,0] [t1>M14;t3,t4>M18;t3,t5,t7,t2>M8;\\1;0.5;0.5;M12 = [13,3,0,0,1,0,0,0] [t1>M15;t6>M16;\\1;1;M13 = [14,2,0,0,0,0,0,1] [t1>M16;t8,t7,t2>M2;\\1;1;M14 = [10,6,1,0,0,0,0,0] [t1>M17;t3,t4>M21;t3,t5,t7,t2>M11;\\1;0.5;0.5;M15 = [12,4,0,0,1,0,0,0] [t1>M18;t6>M19;\\1;1;M16 = [13,3,0,0,0,0,0,1] [t1>M19;t8,t7,t2>M3;\\1;1;M17 = [9,7,1,0,0,0,0,0] [t1>M20;t3,t4>M24;t3,t5,t7,t2>M14;\\1;0.5;0.5;M18 = [11,5,0,0,1,0,0,0] [t1>M21;t6>M22;\\1;1;M19 = [12,4,0,0,0,0,0,1] [t1>M22;t8,t7,t2>M5;\\1;1;M20 = [8,8,1,0,0,0,0,0] [t1>M23;t3,t4>M27;t3,t5,t7,t2>M17;\\1;0.5;0.5;M21 = [10,6,0,0,1,0,0,0] [t1>M24;t6>M25;\\1;1;M22 = [11,5,0,0,0,0,0,1] [t1>M25;t8,t7,t2>M8;\\1;1;M23 = [7,9,1,0,0,0,0,0] [t1>M26;t3,t4>M30;t3,t5,t7,t2>M20;\\1;0.5;0.5;M24 = [9,7,0,0,1,0,0,0] [t1>M27;t6>M28;\\1;1;M25 = [10,6,0,0,0,0,0,1] [t1>M28;t8,t7,t2>M11;\\1;1;M26 = [6,10,1,0,0,0,0,0] [t1>M29;t3,t4>M33;t3,t5,t7,t2>M23;\\1;0.5;0.5;M27 = [8,8,0,0,1,0,0,0] [t1>M30;t6>M31;\\1;1;M28 = [9,7,0,0,0,0,0,1] [t1>M31;t8,t7,t2>M14;\\1;1;M29 = [5,11,1,0,0,0,0,0] [t1>M32;t3,t4>M36;t3,t5,t7,t2>M26;\\1;0.5;0.5;M30 = [7,9,0,0,1,0,0,0] [t1>M33;t6>M34;\\1;1;M31 = [8,8,0,0,0,0,0,1] [t1>M34;t8,t7,t2>M17;\\1;1;M32 = [4,12,1,0,0,0,0,0] [t1>M35;t3,t4>M39;t3,t5,t7,t2>M29;\\1;0.5;0.5;M33 = [6,10,0,0,1,0,0,0] [t1>M36;t6>M37;\\1;1;M34 = [7,9,0,0,0,0,0,1] [t1>M37;t8,t7,t2>M20;\\1;1;M35 = [3,13,1,0,0,0,0,0] [t1>M38;t3,t4>M42;t3,t5,t7,t2>M32;\\1;0.5;0.5;M36 = [5,11,0,0,1,0,0,0] [t1>M39;t6>M40;\\1;1;M37 = [6,10,0,0,0,0,0,1] [t1>M40;t8,t7,t2>M23;\\1;1;M38 = [2,14,1,0,0,0,0,0] [t1>M41;t3,t4>M45;t3,t5,t7,t2>M35;\\1;0.5;0.5;M39 = [4,12,0,0,1,0,0,0] [t1>M42;t6>M43;\\1;1;M40 = [5,11,0,0,0,0,0,1] [t1>M43;t8,t7,t2>M26;\\1;1;M41 = [1,15,1,0,0,0,0,0] [t1>M44;t3,t4>M47;t3,t5,t7,t2>M38;\\1;0.5;0.5;M42 = [3,13,0,0,1,0,0,0] [t1>M45;t6>M46;\\1;1;M43 = [4,12,0,0,0,0,0,1] [t1>M46;t8,t7,t2>M29;\\1;1;M44 = [0,16,1,0,0,0,0,0] [t3,t4>M49;t3,t5,t7,t2>M41;\\0.5;0.5;M45 = [2,14,0,0,1,0,0,0] [t1>M47;t6>M48;\\1;1;M46 = [3,13,0,0,0,0,0,1] [t1>M48;t8,t7,t2>M32;\\1;1;M47 = [1,15,0,0,1,0,0,0] [t1>M49;t6>M50;\\1;1;M48 = [2,14,0,0,0,0,0,1] [t1>M50;t8,t7,t2>M35;\\1;1;M49 = [0,16,0,0,1,0,0,0] [t6>M51;\\1;M50 = [1,15,0,0,0,0,0,1] [t1>M51;t8,t7,t2>M38;\\1;1;M51 = [0,16,0,0,0,0,0,1] [t8,t7,t2>M41;\\1;

Caracteristicele de performan:

2D3D

P1

P3

P5

P8

P6

Concluzii: n urma efecturii lucrrii date de laborator am obinut experien n domeniul studierii metodelor de descriere i de evaluare a sistemelor de ateptare prioritare i cu performanele programului Visual Petry Net+.


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