Large-deviations analysis of the fluid approximation for a controllable tandem queue
The paper considers a discrete-time tandem queueing network of two single-server queues, Bernoulli \((\lambda)\) arrivals, Bernoulli (\(\mu_1\) and \(\mu_2\)) servers and infinite buffers. The state of the network at time \(n\) is \(\xi^n= (\xi^n_1, \xi^n_2)\), where \(\xi^n_i\) is the number of customers in buffer \(i\). At each moment of time \(n\), a server \(i\) either serves a customer from its buffer \((a^n_i=1)\) or is idle \((a^n_i= 0)\). The value function of the process under control \(a= \{(a^n_1, a^n_2),\, n= 0,1,\dots\}\) is defined as \[ V_a(x(N)):= E^a_{x(N)} \sum^{T_n}_{n=0} (\xi^n_1 c_1+ \xi^n_2 c_2), \] where \(E^a_{x(N)}(\cdot)\) denotes the expectation given initial state \(x(N)\) and control \(a\). The discrete optimal control is \(V_a(x(N))\to \min\). To solve this problem, a fluid approximation is constructed. This approximation is used to get the first term of the asymptotic of the value function of the optimal policy. The main theorem of the paper gives the next term of the asymptotic.
scientific article; zbMATH DE number 2063744
scientific article