TY - JOUR
T1 - Erlang arrivals joining the shorter queue
AU - Adan, I.J.B.F.
AU - Kapodistria, S.
AU - Leeuwaarden, van, J.S.H.
PY - 2013
Y1 - 2013
N2 - We consider a system in which customers join upon arrival the shortest of two single-server queues. The interarrival times between customers are Erlang distributed and the service times of both servers are exponentially distributed. Under these assumptions, this system gives rise to a Markov chain on a multi-layered quarter plane. For this Markov chain we derive the equilibrium distribution using the compensation approach. The expression for the equilibrium distribution matches and refines tail asymptotics obtained earlier in the literature.
AB - We consider a system in which customers join upon arrival the shortest of two single-server queues. The interarrival times between customers are Erlang distributed and the service times of both servers are exponentially distributed. Under these assumptions, this system gives rise to a Markov chain on a multi-layered quarter plane. For this Markov chain we derive the equilibrium distribution using the compensation approach. The expression for the equilibrium distribution matches and refines tail asymptotics obtained earlier in the literature.
U2 - 10.1007/s11134-012-9324-8
DO - 10.1007/s11134-012-9324-8
M3 - Article
VL - 74
SP - 273
EP - 302
JO - Queueing Systems: Theory and Applications
JF - Queueing Systems: Theory and Applications
SN - 0257-0130
IS - 2-3
ER -