On a tandem queue with batch service and its applications in wireless sensor networks

We present a tandem network of queues \(0,\dots , s-1.\) Customers arrive at queue 0 according to a Poisson process with rate \(\lambda \). There are s independent batch service processes at exponential rates \(\mu _0, \dots , \mu _{s-1}\). Service process i, \(i=0, \dots , s-1\), at rate \(\mu _i\) is such that all customers of all queues \(0, \dots , i\) simultaneously receive service and move to the next queue. We show that this system has a geometric product-form steady-state distribution. Moreover, we determine the service allocation that minimizes the waiting time in the system and state conditions to approximate such optimal allocations. Our model is motivated by applications in wireless sensor networks, where s observations from different sensors are collected for data fusion. We demonstrate that both optimal centralized and decentralized sensor scheduling can be modeled by our queueing model by choosing the values of \(\mu _i\) appropriately. We quantify the performance gap between the centralized and decentralized schedules for arbitrarily large sensor networks.