Summary: On the non-optimality of LAS
within the class IMRL
Samuli Aalto (Helsinki University of Technology)
Urtzi Ayesta (LAAS-CNRS)
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: Non-preemptive 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

Source: Ayesta, Urtzi - Laboratoire d'Analyse et d'Architecture des Systèmes du CNRS

Collections: Engineering