Forms resuming sheet

Pagina 1

Symbols n=number of customers in the whole system; λ=arrival rate; µ=service rate; N=maximum number of customers in the system; c=number of servers; Pn=probability there are n customers in the system; Ls=average number of customers in the system; Lq=average number of customers waiting in the queue; Lb=average number of customers in a queue in a busy system; Ws=average time spent by a customer in the system; Wq=average time spent by a customer in the queue; Wb=average time spent in a queue by a customer in a busy system Standard Model M/M/1 (0< ρ<1) Standard Model M/M/c (0< ρ<c) 1 o i! c!(1−  /c) + P0=1- ρ P =   c−1  i   c kP(n  k) =   i=0   n P per 0  n  c n! o nPn = P0  − sL =  Pn Lq =  − c!cn−c P0  n per n c Lb =  − c cP(n  c) = P c!(c − ) o 1Ws =  −  Ls = (c −1)!(c −  )2 P0 +  c+1  − =  qW q sL = L −  1  − bW = Lq P(n c)bL = 1Lq Lq Ws =  +  Wq =  P(n c) Wq bW = Standard M/G/1 (V(t) = service time variance) s qL = L +   2 + 2V(t) 2(1− )Lq =  s LW = s  q b LW = Ws with Prehemptive priority Ws with NON Prehemptive priority Model M/M/1 limited queue Model M/M/c limited queue (0< ρ<c) 1−  N+1 1−  per        +   N i−c o c P =  i=c+1  i=0  c!  1  i!  i  c−1  i  1 P0= 1 N +1 per  =  P n! o  n per 0  n  c P(n  0) =1− P0 Pn= nPn = P0 per n≤N c!cn−c P0  n per c  n N 1−  N+11−   − (N +1) N +1 per   0 c−1 i=0 P(n  c) =1− P i! i Ls= N 2 per  =   c  c   c     N −c      N−c − (N − c)(c −1)!(c − )2  P c+1 Ls = 0 1− 1−  +  (1−PN ) Lq = Ls − (1−P0 ) Lq = Ls −  (1−PN ) 01− P Lq bL = Lq P(n c)bL = + 1 N(1− P )  Lq sW = + 1 N(1− P )  Lq sW =  − 1 q sW = W  − 1 q sW = W 01− P Wq bW = P(n c) Wq bW = Self Service Model M/G/∞ (e=2.718) ne−  Pn =…