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MGST 391 > Queuing > Flashcards

Queuing Flashcards

1
Q

why do we have queues?

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

why should businesseses care about queus?

A

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

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3
Q

what is the question that companies face cuz of queus?

A

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

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4
Q

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

A

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

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5
Q

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

A

increases!!
decreases

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6
Q

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

A

-decreases
-increases

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7
Q

What measurements do we consider in queuing theory

A

increase/decrease

of servers
customer arrival rates

or reduce average service time

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8
Q

is queuing theory for bpr or cpi

A

cpi!

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9
Q

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

A

-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)

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10
Q

what are lines also for

A

printers
manufacturing
e messaging
people

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11
Q

who begin queuing theory

A

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

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12
Q

Q management- first 5 suggestions for businesses

A
  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)
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13
Q

queing- second set of suggestions for sbuiness (5)

A
  1. modify arrival behaviour
    -motivate ppl to come outside of peak hours (incentives like happy hour)
  2. idle resources out of sight
    -good to keep idle things like cash registers out of sight
  3. segment customers
    -sometimes ppl wanna pay extra to wait less
    -have an express lane (volume of purchase considerations)
  4. think long term
    -long waits will immpact business
    -word of mouth can multiply impact
  5. a friendly server (alter impressions of wait)
    -have nice staff
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14
Q

disney management of queues

A
  • post waiting times of queues outside
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15
Q

disney themepark- fast pass system

A

the coupon tells you when to return!!!

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16
Q

how does disney manage queue expectations in the hotel

why?

A

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

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17
Q

virtual queues example - restaurants

A

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

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18
Q

what are the arrivals in a queing system coming from

A

calling population

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19
Q

what is the protocol that many queing systems folloe

A

FCFS (first come first serve)

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20
Q

what are 3 characterisitcs of a calling population

A

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

every characteristic leads to alt

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21
Q

size alts in calling population characteristics

A

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!

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22
Q

arrival pattern alts in calling population characteristics

A

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

pre determined: appointments/ reservations

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23
Q

attitude alts in calling population characteristics

A

patient: people want to wait for service

impatient: people leave without getting service
-balking
-reneging

24
Q

what are the two ways we can define queuing systems

A
  • either by the # of channels (Servers)
  • or the # of phases
25
Q

what is the single server single phase q system

A

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

26
Q

visual of a single server single phase system configuration

A

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

27
Q

of servers?

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

A

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

28
Q

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

A

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

29
Q

what does the multi server single phase look like

A

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!!!

30
Q

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

A

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)

31
Q

why do we use random variables in queuing?

A

BECUASE custoemrs will arrive in the system at a random time

32
Q

when a customer arrives randomly, and a server is idle what happens

-if all busy?

A

they get served immediately

-wait in queue

33
Q

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

A

they ARE REENEGED

34
Q

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

A

BALKED

35
Q

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

A
36
Q

what are the 2 key events in the line ups?

A

-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

37
Q

unit of lambda, meaning

A

customers/ minute, average arriival rate

38
Q

unit of mu

A

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

39
Q

IF mu > lambda(service rate > arrival rate), then service time<interarrival time… so//

A

you shouldnt theoretically have a queue

BUT lambda is only an ideal estimation!!! customers dont arrive exactly per the distribution!!

40
Q

how to determine interarrival rate given lambda?

A

1/lambda

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

41
Q

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

A

1/mu

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

42
Q

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

A

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

43
Q

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

A

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

LAMBDA

44
Q

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

A

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

45
Q

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

A

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

46
Q

we measure randomness in 2 variables!!

A

lambda (Arrival rate)

mu (Service rate)

47
Q

what is the service rate (mu)

A

of customer one server can manage in a time period

48
Q

what is the avg service time

A

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

49
Q

what is the distribution for the service rate?

what is the distribution for the avg service time?

A

poisson!! (integer)

exppoenntial (continuous)

50
Q

is service time always gonna be 1/mu

A

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

51
Q

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

A

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)

52
Q

what are two sources of randomness in the queeuing system?

A

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

53
Q

what is the kendall notaiton?

A

-developed to descrive queuing models

you need 3 things
1. prob dis of arrival times
2. prob dis of service times
3. # of servers

54
Q

kendall notation : M/M/1 meaning

A

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)

55
Q

what does it mean for the first M in MM1

A

means that the arrival process dist is in poisson

56
Q

what does it mean for the second M in MM1

A

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

57
Q
A

MGST 391 (13 decks)

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