Queuing

Question 1

why do we have queues?

Answer 1

1. not enough servers
2. servers too slow
3. too many customers
4. lineup

Question 2

why should businesseses care about queus?

Answer 2

because reducing aount of times wasted in lines will be good!

Question 3

what is the question that companies face cuz of queus?

Answer 3

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

Question 4

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

Answer 4

the lowest point on TEC curve= highest level of service without too much cost

Question 5

As service levels increase:
-what happens to the cost of providing the service
-what happens to the cost of customer dissatisfaction

Answer 5

increases!!
decreases

Question 6

As service levels decreaes:
-what happens to the cost of providing the service
-what happens to the cost of customer dissatisfaction

Answer 6

-decreases
-increases

Question 7

What measurements do we consider in queuing theory

Answer 7

increase/decrease

of servers
customer arrival rates

or reduce average service time

Question 8

is queuing theory for bpr or cpi

Answer 8

cpi!

Question 9

what are 5 actions customers do in a lineup
“customer strategies”

Answer 9

-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)

Question 10

what are lines also for

Answer 10

printers
manufacturing
e messaging
people

Question 11

who begin queuing theory

Answer 11

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

Question 12

Q management- first 5 suggestions for businesses

Answer 12

1. perceptions of wait: people over estimate their wait time (they think they are waiting longer than they are)
2. 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)
3. businesses should provide distractions
   - smthg to do/ watch/read
4. businesses should AVOID line ups where possible
   -reservations, appointments, automations etc
5. 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)

Question 13

queing- second set of suggestions for sbuiness (5)

Answer 13

6. modify arrival behaviour
   -motivate ppl to come outside of peak hours (incentives like happy hour)
7. idle resources out of sight
   -good to keep idle things like cash registers out of sight
8. segment customers
   -sometimes ppl wanna pay extra to wait less
   -have an express lane (volume of purchase considerations)
9. think long term
   -long waits will immpact business
   -word of mouth can multiply impact
10. a friendly server (alter impressions of wait)
    -have nice staff

Question 14

disney management of queues

Answer 14

• post waiting times of queues outside

Question 15

disney themepark- fast pass system

Answer 15

the coupon tells you when to return!!!

Question 16

how does disney manage queue expectations in the hotel

why?

Answer 16

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

Question 17

virtual queues example - restaurants

Answer 17

restaurants will text you when they have a table ready for you!!!

Question 18

what are the arrivals in a queing system coming from

Answer 18

calling population

Question 19

what is the protocol that many queing systems folloe

Answer 19

FCFS (first come first serve)

Question 20

what are 3 characterisitcs of a calling population

Answer 20

1) size
3) arrival pattern
3) attitude of customers who arrive through it

every characteristic leads to alt

Question 21

size alts in calling population characteristics

Answer 21

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!

Question 22

arrival pattern alts in calling population characteristics

Answer 22

random: # of independant variables
-could model as poisson or other

pre determined: appointments/ reservations

Question 23

attitude alts in calling population characteristics

Answer 23

patient: people want to wait for service

impatient: people leave without getting service
-balking
-reneging

Question 24

what are the two ways we can define queuing systems

Answer 24

• either by the # of channels (Servers)
• or the # of phases

Question 25

what is the single server single phase q system

Answer 25

one server, you get the service and you leave (single banking machine, car wash, sstore w one cashier

Question 26

visual of a single server single phase system configuration

Answer 26

arrivals -> queue -> service facility -> departures after services

Question 27

# of servers? single server, multiphase # of processes? visual? example?

Answer 27

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

Question 28

multi server, single phase # server # of processes? visual? example?

Answer 28

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

Question 29

what does the multi server single phase look like

Answer 29

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!!!

Question 30

multi server, multiphase # of processes? # esrvers? visual? example?

Answer 30

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)

Question 31

why do we use random variables in queuing?

Answer 31

BECUASE custoemrs will arrive in the system at a random time

Question 32

when a customer arrives randomly, and a server is idle what happens -if all busy?

Answer 32

they get served immediately -wait in queue

Question 33

if the customers join the queue then leave without being served?

Answer 33

they ARE REENEGED

Question 34

if the customers look at the queue and realize that the line is too long and dont join they?

Answer 34

BALKED

Question 35

It takes the service time to process the customer who leaves the system when finished

Question 36

what are the 2 key events in the line ups?

Answer 36

-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

Question 37

unit of lambda, meaning

Answer 37

customers/ minute, average arriival rate

Question 38

unit of mu

Answer 38

customers/minute, how long does it take to serve them on average

Question 39

IF mu > lambda(service rate > arrival rate), then service time

Answer 39

you shouldnt theoretically have a queue BUT lambda is only an ideal estimation!!! customers dont arrive exactly per the distribution!!

Question 40

how to determine interarrival rate given lambda?

Answer 40

1/lambda if lambda=2, 2 customers every minute, then 1/lambda (1/2 minute) between customers arriving

Question 41

how to determine how long average service time will take given mu?

Answer 41

1/mu if serving 3 customers per minute, then 1/3 minutes is service time!

Question 42

the time between arivals is ==== and this is why ----

Answer 42

independant, and this is why on average it may be a specific amount of arrivals but this not always true

Question 43

what distributuon do we use for the arrival rate (and why?)

Answer 43

we use the poisson discrete distribution because arrival rate has to be a integer (# of people arriving per minute) LAMBDA

Question 44

what distributuon do we use for the INTER-arrival rate (and why?)

Answer 44

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

Question 45

Poisson probability distribution of arrival rates -formula -meaning -use

Answer 45

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

Question 46

we measure randomness in 2 variables!!

Answer 46

lambda (Arrival rate) mu (Service rate)

Question 47

what is the service rate (mu)

Answer 47

of customer one server can manage in a time period

Question 48

what is the avg service time

Answer 48

the average time required to provide service (inter service time) = 1/mu

Question 49

what is the distribution for the service rate? what is the distribution for the avg service time?

Answer 49

poisson!! (integer) exppoenntial (continuous)

Question 50

is service time always gonna be 1/mu

Answer 50

NO!!! its not it is an average and this can change

Question 51

Poisson probability distribution of service times -formula -meaning -use

Answer 51

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)

Question 52

what are two sources of randomness in the queeuing system?

Answer 52

randomness in when teh customers arrive and randomness in teh service time

Question 53

what is the kendall notaiton?

Answer 53

-developed to descrive queuing models you need 3 things 1. prob dis of arrival times 2. prob dis of service times 3. # of servers

Question 54

kendall notation : M/M/1 meaning

Answer 54

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)

Question 55

what does it mean for the first M in MM1

Answer 55

means that the arrival process dist is in poisson

Question 56

what does it mean for the second M in MM1

Answer 56

means that the service time is exponential!!!! differenet meaning for first and second M