Queuing Flashcards
why do we have queues?
- not enough servers
- servers too slow
- too many customers
- lineup
why should businesseses care about queus?
because reducing aount of times wasted in lines will be good!
what is the question that companies face cuz of queus?
what level of service should they provide?
tradeoff: more service (more servers), but expensive, but happy customers
or LESS SERVICE (less servers), cheaper, unhappy customers
That one graph!! analyze
RED LINE: cost of providing service (increasing)
GREEN LINE: cost of waiting time (decreasing)
BLACK LINE: total expected cost (sum)
what point do we care about/optimal point
the lowest point on TEC curve= highest level of service without too much cost
As service levels increase:
-what happens to the cost of providing the service
-what happens to the cost of customer dissatisfaction
increases!!
decreases
As service levels decreaes:
-what happens to the cost of providing the service
-what happens to the cost of customer dissatisfaction
-decreases
-increases
What measurements do we consider in queuing theory
increase/decrease
of servers
customer arrival rates
or reduce average service time
is queuing theory for bpr or cpi
cpi!
what are 5 actions customers do in a lineup
“customer strategies”
-wait
-not join
-jockey (Change line)
-join then leave
-meld (2 people who separate into two lines, and whoever gets there first the other person goes with that one)
what are lines also for
printers
manufacturing
e messaging
people
who begin queuing theory
ERLANG! engineer was looking at congestion of waiting times (and you had to wait too long to go through the operator)
deals with waiting times
Q management- first 5 suggestions for businesses
- perceptions of wait: people over estimate their wait time (they think they are waiting longer than they are)
- business needs to determine what the acceptable wait times are
depends on busines type
- type of service (bank u can wait, ER no)
- type of waiing (irl or over the phone)
- type of customer (parent w small kids etc) - businesses should provide distractions
- smthg to do/ watch/read - businesses should AVOID line ups where possible
-reservations, appointments, automations etc - consider if you should tell the customer wait time
-do this only if customer is unable to estimat ethe wait time themselves (phone support or plane waiting for takeoff)
queing- second set of suggestions for sbuiness (5)
- modify arrival behaviour
-motivate ppl to come outside of peak hours (incentives like happy hour) - idle resources out of sight
-good to keep idle things like cash registers out of sight - segment customers
-sometimes ppl wanna pay extra to wait less
-have an express lane (volume of purchase considerations) - think long term
-long waits will immpact business
-word of mouth can multiply impact - a friendly server (alter impressions of wait)
-have nice staff
disney management of queues
- post waiting times of queues outside
disney themepark- fast pass system
the coupon tells you when to return!!!
how does disney manage queue expectations in the hotel
why?
green mickey ears- 7-8 am no busy
yellow mickey ears- 8-9 am, things are a bit busier
red mickey ears- 9-11 am busiest time and wait
managing their expectations avoids sadness
virtual queues example - restaurants
restaurants will text you when they have a table ready for you!!!
what are the arrivals in a queing system coming from
calling population
what is the protocol that many queing systems folloe
FCFS (first come first serve)
what are 3 characterisitcs of a calling population
1) size
3) arrival pattern
3) attitude of customers who arrive through it
every characteristic leads to alt
size alts in calling population characteristics
Finite: pre-set max
Infinite: most often we assume this!! because size can grow forever
-ex: # of ppl in line is small compared to those that could come!
arrival pattern alts in calling population characteristics
random: # of independant variables
-could model as poisson or other
pre determined: appointments/ reservations
attitude alts in calling population characteristics
patient: people want to wait for service
impatient: people leave without getting service
-balking
-reneging
what are the two ways we can define queuing systems
- either by the # of channels (Servers)
- or the # of phases
what is the single server single phase q system
one server, you get the service and you leave (single banking machine, car wash, sstore w one cashier
visual of a single server single phase system configuration
arrivals -> queue -> service facility -> departures after services
of servers?
single server, multiphase
# of processes?
visual?
example?
1 server
many processes
arrivals -> queue-> type 1 service facility -> queue-? type 2 service facility -> departures after services
ex: drive through at mcdonalds, starbucks, assembly line
multi server, single phase
# server
# of processes?
visual?
example?
multiple
1 process
arrivals-> queue -> -> -> service facility 1 service faiclity 2 service facilitt 3 -> departures after service
EX: banking, tellers or bank machines, check at airport, fastfood restauttuanr
what does the multi server single phase look like
basicall you arent lining up behind each server,
its like one line up!! and then once you get to the front you can go to any server!!!
multi server, multiphase
# of processes?
# esrvers?
visual?
example?
many
many
complex:
arrivals-> queue-> type 1 facility-> type 2 faciltiy (but theres two of each)-> departures after services
ex: health card, auto repair, job shop (non linear)
why do we use random variables in queuing?
BECUASE custoemrs will arrive in the system at a random time
when a customer arrives randomly, and a server is idle what happens
-if all busy?
they get served immediately
-wait in queue
if the customers join the queue then leave without being served?
they ARE REENEGED
if the customers look at the queue and realize that the line is too long and dont join they?
BALKED
It takes the service time to process the customer who leaves the system when finished
what are the 2 key events in the line ups?
-arrival rate (how often they arrive) (lambda)
#/ unit of time
-service time (how long it takes to get the service) (mu)
how many they can serve
unit of lambda, meaning
customers/ minute, average arriival rate
unit of mu
customers/minute, how long does it take to serve them on average
IF mu > lambda(service rate > arrival rate), then service time<interarrival time… so//
you shouldnt theoretically have a queue
BUT lambda is only an ideal estimation!!! customers dont arrive exactly per the distribution!!
how to determine interarrival rate given lambda?
1/lambda
if lambda=2, 2 customers every minute, then 1/lambda (1/2 minute) between customers arriving
how to determine how long average service time will take given mu?
1/mu
if serving 3 customers per minute, then 1/3 minutes is service time!
the time between arivals is ==== and this is why —-
independant, and this is why on average it may be a specific amount of arrivals but this not always true
what distributuon do we use for the arrival rate (and why?)
we use the poisson discrete distribution because arrival rate has to be a integer
(# of people arriving per minute)
LAMBDA
what distributuon do we use for the INTER-arrival rate (and why?)
exponential because this is a conntinuous desitribution (this is # of minutes before customers pull up so it could be minutes or seconds)
CONTINUOUS
1/LAMBDA
Poisson probability distribution of arrival rates
-formula
-meaning
-use
P(x)= lambda ^(x) * e^-lambda/ x!
x= number of arrivals in time period (givn value in question)
lambda= mean number of arrivals per time period (established average)
what is the probability of x amount of customers showing up when the average is lambda
we measure randomness in 2 variables!!
lambda (Arrival rate)
mu (Service rate)
what is the service rate (mu)
of customer one server can manage in a time period
what is the avg service time
the average time required to provide service (inter service time) = 1/mu
what is the distribution for the service rate?
what is the distribution for the avg service time?
poisson!! (integer)
exppoenntial (continuous)
is service time always gonna be 1/mu
NO!!! its not it is an average and this can change
Poisson probability distribution of service times
-formula
-meaning
-use
P(Service time <=t)= 1-e ^-mu*t
t=given in the question
mu= customers/ hour
NOTE: t and mu must be same units
probability that service time is less than or equal to a time that we care about!! (and then you can see how much is the prob of being greater than time given)
what are two sources of randomness in the queeuing system?
randomness in when teh customers arrive and randomness in teh service time
what is the kendall notaiton?
-developed to descrive queuing models
you need 3 things
1. prob dis of arrival times
2. prob dis of service times
3. # of servers
kendall notation : M/M/1 meaning
M/M/1
First M: proability dist for arrival process
Second M: probability dist for service times
#: # of servers
M= markovian (poisson for rates, exponential for times)
G= any dist
D= deterministic service times (not random)
what does it mean for the first M in MM1
means that the arrival process dist is in poisson
what does it mean for the second M in MM1
means that the service time is exponential!!!! differenet meaning for first and second M
