Queue Management Systems (QMS) are designed to manage customer flow by improving process optimization and wait time reduction, streamlining the queuing experience.

Operation management

1. @Stoct socieing
Mode! I :(M/M/1) (oo /FCFs)
os fointh amd Death Madel
A
Mean arsival Tate (mo. o
arival er
unit time)
= Meon
Sesvice ate (no. o
customer sesved pes
unit time)
oTsokic tmtenstH
he
system Ls
Ebected
(avesage)
no. o
unets m 4he Sstem
Ls
Ls .
ud Epec te d (average)
uue lemgth Le
L= Ls
(H-)
ivExheched tloi ting
the queua, Na,
Um

2. Exhected daing
Line n he System, Ws
@Stoet PaocBicing
w Expected (u Expected waiking
time oh
a Customea who has to wait (w/w7o)
(w/W >o)= -
(v) Expected lengBh omom-emt 9,uua
(LJL7O)
=
u-a
m) Fsobabi lH4 ob Waiting
time
in the
que
2t on) Paobabi lidg
a(1-a)e(K-3)n,
dW
uaue Size 2 N = f"
P(
a)
e"(4-
a)w
dw

3. @stavd aac ticung
(Poobabi lik (lai king
tine
n he system 2 )
f4-2)e
(H-A)w
dw
t
Ltles forvmulas
Ls A Ws
a,= s

4. Stoct Psocicing
Q: A
exponental distibution with
:A TV. me chamic fnds that ha tume spent on his Tobs has an
Tv.
mean 30 muinutes, ih he epairs
Sets in the o7der in which hey Come in.
1 he
oisson with on
asoival o
aNexage
gate o
lo
mec haniS expected idle
day?
Houw many Jobs ase ahead o he awexoge
sets is appsoximately
pea
me each
eight-hous da,
what is the
da?
Just bouaht in ?
man
Sets
30
10
Solution :
48 48
30 8 X60
Expected no. ot Jobs
48
Ls -A L
48 30
5
L
3
Ls
48-30
s1Jobs. 30 ky8

5. Stort Psacicun
the action o
he teme
the mechanicd is
busy the
Smce
emaums busy
he
no.
ok hous o
which the epaisman
erg bt-
houwt day in
8x
=
5 houns
48
idle
tma toft
ohich
e
mechamic
semain
me
m
PSemam
Therceph, the =8-5) hoors.
egh-hou day
= 3 hou»s.