Lecture 8
Basic Performance Results, cont'd

• Little's Law: N = R * X
• and examples ...
• Queuing Time, Service Demand, Residence Time, Response Time
• Applying Little's Law to the Waiting Line
• Applying Little's Law to the Queue
• Applying Little's Law to the Server
• Interactive Response Time Law: R = (M / X_0) - Z
  • R: average response time
  • Z: average think time
  • X_0: average throughput
  • M: number of sources of requests
• Interative Response Time law, derived
• Interative Response Time law, example
• Throughput Bound:
  • The utilization of a resource cannot exceed 100%:
    

    
    		X_0 = U_i / D_i
    
    	            <=  1 / D_i
    
    This is the upper asymptotic bound on throughput under heavy load conditions.
    

• Throughput Bound:
  • Apply Little's Law to the entire system:
    

    
    		N =  R * X_0  >=   Sum, i=1 to k (D_i) * X_0
    
    		  =>  X_0 <=  N /  Sum, i=1 to k (D_i) 
    
    This is the upper asymptotic bound on throughput under light load conditions.
    

• Throughput Bound:

  
  		X_0 <= min [ (1 / max{D_i}) , (N / Sum i=1 to K (D_i)) ]