We consider a GI/M/1 queueing system in which the server takes exactly one exponential vacation each time the system empties. We derive the PGF of the stationary queue length and the LST of the stationary FIFO sojourn time. We show that both the queue length and the sojourn time can be stochastically decomposed into meaningful quantities.

We consider the estimation of arrival and service rates for queues based on queue length data collected at successive, not necessarily equally spaced, time points. In particular, we consider the M/M/c queue, for c large, but application of the method to the repairman problem is almost identical, and the general approach presented should extend to other queue types. The estimation procedure make...

We study the synchronization in the context of network traffic on a 2-d communication network with local clustering and geographic separations. The network consists of nodes and randomly distributed hubs where the top five hubs ranked according to their coefficient of betweenness centrality (CBC) are connected by random assortative and gradient mechanisms. For multiple message traffic, messages...

A single-server queueing system with a batch Markovian arrival process (BMAP) and MAP-input of disasters causing all customers to leave the system instantaneously is considered. The system has two operation modes, which depend on the current queue length. The embedded and arbitrary time stationary queue length distribution has been derived and the optimal control threshold strategy has been det...

We show that the length of a queue communicates information about the quality of a product when some consumers are uninformed. In turn, a firm may strategically choose its service rate to signal its quality through the queue. In our setting, a firm may have high or low quality and sells a good to consumers who are heterogeneously informed. The firm may choose a slow or (at a cost) a fast servic...

In this paper we study a MAP/M/K system with join-the-shortest-queue (JSQ) discipline which consists of K servers and K queues with infinite buffers. An arrival joins the shortest queue and in the case that there are n (n≤ K) queues having the same shortest length, the customer will join any one of these shortest queues with probability 1/n. We model the system as a levelexpanding QBD (LDQBD) p...

We analyze the dynamic behavior of a single RED controlled queue interacting with a large population of idealized TCP sources, i.e., sources obeying the rules of linear increase and multiplicative decrease. The aggregate traffic from this population is modeled in terms of the time dependent expected value of the packet arrival rate which reacts to the packet loss taking place in the queue. The ...

We consider a system of two parallel queues sharing a common arrival process, where the arriving customers select which queue to join based on a generalized Join the Shortest Queue ( ) policy. We assume that both servers run at the same speed. However, we assume that departing customers face some additional delay after leaving the system, and that this downstream delay is different between the ...

We consider a model of two M/M/1 queues, served by a single server. The service policy for this polling model is of threshold type: the server serves queue 1 exhaustively, and does not remain at an empty queue if the other one is non-empty. It switches from queue 2 to queue 1 when the size of the latter queue reaches some level T , either preemptively or non-preemptively. All switches are insta...