Summary: On the nonoptimality of LAS
within the class IMRL
Samuli Aalto (Helsinki University of Technology)
Urtzi Ayesta (LAASCNRS)
Scheduling in a M/G/1 Queue
Poisson arrivals with rate . Service requirements are i.i.d. with
distribution F(x)=P[X x].
Attained service is known (total service requirement unknown)
Optimality criterion: Mean number of jobs in the system
service requirement
server
Monotonous Hazard Rate
Hazard rate of a distribution function: h(x)dx=P[x< X x+dx  X > x]
IHR: Nonpreemptive discipline (FCFS etc.)
Exponential: M/M/1 Mean number of jobs is policy independent
DHR: Least Attained Service (LAS) is optimal. The job(s) who has
attained the least amount of service is served.
( ) ( )
( )xF
xf
