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UID:www.tcs.tifr.res.in/event/1260
DTSTAMP:20230914T125956Z
SUMMARY:Heterogeneous arrival streams in a two-queue network
DESCRIPTION:Speaker: Agniv Bandyopadhyay\n\nAbstract: \nIn a concert queuin
g game\, users decide when to arrive at a bottleneck queue of constant cap
acity that opens at a specific time. Every user wants to simultaneously mi
nimize her waiting time and get served as early as possible. In previous i
ncarnations\, this game has been studied over a single queue and over netw
orks with specific topologies such as tandem networks\, trellis networks\,
and general feed-forward networks having multiple layers\, with users arr
iving at one extreme layer and traveling to the other extreme. A unique no
n-cooperative Nash Equilibrium profile has been identified in the case of
the single queue and tandem networks with multiple layers. Whereas for tre
llis networks and general feed-forward networks\, the existence of non-coo
perative Nash Equilibrium profiles has been proved. It has also been prove
n that if there are multiple such equilibriums\, they will all have an equ
al social cost. In this project\, we attempt to study the situation where
multiple classes of players are traveling through different paths in a que
uing network. For simplicity\, we consider two groups of players who inten
d to travel on two distinct paths in a two-queue network. We also assume t
hat all players in a group have identical preferences. In all these instan
ces\, we can find a unique non-cooperative Nash Equilibrium profile as lon
g as the two groups have different preferences. Also\, in equilibrium\, th
e two groups will choose their order of arrival depending on how their pop
ulation sizes compare. We also observe that whenever the two groups share
one queue in their path\, if the queue's capacity is under an identified t
hreshold\, the two groups will arrive in that queue in contiguous disjoint
intervals. On the other hand\, if it is strictly above that threshold\, t
he two groups will arrive together in that queue over some contiguous inte
rval in the equilibrium profile.\n
URL:https://www.tcs.tifr.res.in/web/events/1260
DTSTART;TZID=Asia/Kolkata:20221223T160000
DTEND;TZID=Asia/Kolkata:20221223T170000
LOCATION:A201
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