Operations Notes – Waiting and Service Quality

• Waiting can significantly increase throughput time
• Same duration of wait may mean different things to customers in different environments
• Unoccupied time feels longer than occupied time

⇒ Pre-process time longer than in-process time

• Anxiety makes the wait seem even longer
• Uncertain waits are worse than certain waits (How long will the wait be?)
• Unexplained waits are worse than explained waits (What is the cause of the wait?)
• Unfair waits are longer than equitable waits
• More valuable service allows longer acceptable waits (Queue specialization)
• Solo waits are longer than group waits

Variability causes waiting
⇒ When variability is present, a queue will result even if avg. arrival rate (λ) < avg. service rate (μ)

λ = average arrival rate
μ = average service rate
ρ = flow intensity of the system
W_q = average waiting time
L_q = average queue length
L = average number in the system
W = average time in the system
U = utilization (1-U = idle time)
M = the number of service providers

ρ = λ/μ
W_q = L_q /λ
L_{q =} W_{q *} λ
L = L_q + ρ
W = W_q + 1/μ = L_q/λ + 1/μ
U = λ/Mμ

There is a trade-off between cost and waiting times. Returns from adding capacities are significantly higher when utilization is brought down from 95% to 90% than from 85% to 80% (set Utilization to less than or equal to 90%):

Good News: initial improvements are easy
Bad News: diminishing marginal returns

Decision variables when designing a queuing system:

• target waiting time
• number of stages
• queue discipline
• level of worker training

Channels are the number of parallel windows open (M)
Lines are the number of waiting lines
Stages are the number of windows a customer gets serviced at

Reduce/Improve waiting times by:

• hiring more workers
• training workers or taking other steps to improve productivity
• shaping customer demand
• use psychology principles to lower perceived waiting times