04 Utilization

One Processor, one job type

Utilization Analysis
 Utilization (u) = fraction of time a resource is busy.
 Calculate u for each resource as shown on

following slides.
 In a network (i.e., system) where jobs flow through

multiple resources, the one with the highest u is the
“bottleneck.”
 Utilization must be kept below 1 (i.e., 100%), and as we will see later, if there is variability then u may need to even be kept significantly below 100%.
 The system capacity is the job flow rate R that yields u = 100% at the bottleneck (unless a lower u is determined necessary for satisfactory operation).

Inventory

Processor

Inventory

(queue of raw materials)

holds
1 job

(finished goods) Departures at rate R

Arrivals at rate R
Interarrival
time
= a =1/R

Inventory
= Iq
Time in queue = Tq

Utilization
=u=R/c=Rp
Actual u cannot exceed 1. If a calculation yields u > 1, it is called ‘implied utilization’.
(The calculation may imply u > 1, but this is not possible.)

Slide ‹#›

Slide ‹#›

Multiple (m) Processors, one job type
Processors

Inventory

Inventory

(queue of raw materials)

(1 job each)

(finished goods) (queue of raw materials)

Inventory
= Iq
Time in queue=Tq …

Interarrival time =1/R

One Processor, multiple (n) job types

Inventory

Arrivals at rate R

Process time = p
Capacity
= c = 1/p

Departures at rate R

Inventory
Processor
(holds 1 job)

Departures at rates
R1, R2,…,Rn

Arrivals at rates
R1, R2,…,Rn

# of processors
=m

(finished goods) For a job of type i,
Process time = pi
Capacity = 1/pi = ci
Utilization for job type i = ui = Ri pi

Process time= p
Capacity
= c = 1/p
Utilization = u = R p / m

Total utilization of each processor = u = u1 + u2 + …. + un

Slide ‹#›

Slide ‹#›

Multiple (m) Processors, multiple (n) job types
Inventory

Processors

Inventory

(queue of raw materials)

(1 job each)

(finished goods) Departures at rates
R1, R2,…,Rn

…

Arrivals at rates
R1, R2,…,Rn

# of processors
=m

For a job of type i,
Process time = pi