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[object Object],1.Practically no congestion­­­—number of vehicles does not exceed five. ,[object Object],2.Number of vehicles waiting is between six to ten
EXPECTED COSTS LEVEL OF SERVICE WAITING COST SERVICE COST TOTAL EXP. COST
BASIC QUEUING PROCESS INPUT SOURCE UNITS CALL  FOR SERVICE QUEUE QUEUE DISCIPLINE SERVICE MECHANISM SERVED UNITS LEAVE
ERLANG’S MODEL: M/M/1: (FIFO/∞/∞) P 0  = Prob. Of zero units in the system=  1   ─  P n  = Prob. Of n units in the system = (  1─  )( n= 0,1,2,3,­­­­­­­­ ) n L = Expected number of units in the system =  ­  W = Expected time spent by a unit in the system =  L  q  = Expected number of units in queue =  W  q  = Expected time spent by a unit in the queue =
A Problem on Model M/M/1 ,[object Object]
Another Problem on Model M/M/1 ,[object Object],[object Object],[object Object]
BASIC RELATIOSHIPS IN QUEUING THEORY ,[object Object],a) SUF<1 b) CONDITION OF STEADY STATE  L  = L  q   = W= W  q  +   L= L  q  +  ------------(1) ------------(2) ------------(3) ------------(4)
MULTI CHANNEL MODEL: M/M/C: (FIFO/∞/∞) P 0=   P n = if  n<= c P n = if  n>=c L  q  =

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Presentation3 modified

  • 1.
  • 2. EXPECTED COSTS LEVEL OF SERVICE WAITING COST SERVICE COST TOTAL EXP. COST
  • 3. BASIC QUEUING PROCESS INPUT SOURCE UNITS CALL FOR SERVICE QUEUE QUEUE DISCIPLINE SERVICE MECHANISM SERVED UNITS LEAVE
  • 4. ERLANG’S MODEL: M/M/1: (FIFO/∞/∞) P 0 = Prob. Of zero units in the system= 1 ─ P n = Prob. Of n units in the system = ( 1─ )( n= 0,1,2,3,­­­­­­­­ ) n L = Expected number of units in the system = ­ W = Expected time spent by a unit in the system = L q = Expected number of units in queue = W q = Expected time spent by a unit in the queue =
  • 5.
  • 6.
  • 7.
  • 8. MULTI CHANNEL MODEL: M/M/C: (FIFO/∞/∞) P 0= P n = if n<= c P n = if n>=c L q =