Stationary remaining service time conditional on queue length

In Mandelbaum and Yechiali (1979) a simple formula is derived for the expected station-ary remaining service time in a FIFO M/G/1 queue, conditional on the number of customers in the system being equal to j, j ≥ 1. Fakinos (1982) derived a similar formula using an alternative method. Here we give a short proof of the formula using rate conservation law (RCL), and generalize to handle higher moments which better illustrates the advantages of using RCL

Gated-type polling systems with walking and switch-in times

We consider models of polling systems where switching times between channels are composed of two parts: walking times required to move from one channel (station) to another, and switch-in times that are incurred only when the server enters a station to render service. We analyze three Gated-type systems: (i) Cyclic polling with Gated regime, (ii) Cyclic polling with Globally-Gated regime, and (iii) Elevator-type polling with Globally-Gated regime. In all systems, the server visits station i if and only if the number of customers (jobs) present there at the gating instant is greater than or equal to a given threshold K i >= 0. For al

An M/G/1 queue with multiple types of feedback and gated vacations

This paper considers a single-server queue with Poisson arrivals and multiple customer feedbacks. If the first service attempt of a newly arriving customer is not successful, he returns to the end of the queue for another service attempt, with a different service time distribution. He keeps trying in this manner (as an `old' customer) until his service is successful. The server operates according to the `gated vacation' strategy: when it returns from a vacation to find $K$ (new and old) customers, it renders a single service attempt to each of them and takes another vacation, etc. We study the joint queue length process of new and old customers, as well as the waiting time distribution of customers. Some extensions are also discussed

Admission control to an M/M/1 queue with partial information

We consider both a cooperative as well as non-cooperative admission into an M/M/1 queue. The only information available is a signal that sais whether the queue size is smaller than some $L$ or not. We first compute the globally optimal and the Nash equilibrium stationary policy as a function of $L$. We compare the performance to that of full information on the queue size. We identify the $L$ that optimizes the equilibrium performanc

Controlled mobility in stochastic and dynamic wireless networks

We consider the use of controlled mobility in wireless networks where messages arriving randomly in time and space are collected by mobile receivers (collectors). The collectors are responsible for receiving these messages via wireless transmission by dynamically adjusting their position in the network. Our goal is to utilize a combination of wireless transmission and controlled mobility to improve the throughput and delay performance in such networks. First, we consider a system with a single collector. We show that the necessary and sufficient stability condition for such a system is given by ρ<1 where ρ is the expected system load. We derive lower bounds for the expected message waiting time in the system and develop policies that are stable for all loads ρ<1 and have asymptotically optimal delay scaling. We show that the combination of mobility and wireless transmission results in a delay scaling of Θ([1 over 1−ρ]) with the system load ρ, in contrast to the Θ([1 over (1−ρ)[superscript 2]]) delay scaling in the corresponding system without wireless transmission, where the collector visits each message location. Next, we consider the system with multiple collectors. In the case where simultaneous transmissions to different collectors do not interfere with each other, we show that both the stability condition and the delay scaling extend from the single collector case. In the case where simultaneous transmissions to different collectors interfere with each other, we characterize the stability region of the system and show that a frame-based version of the well-known Max-Weight policy stabilizes the system asymptotically in the frame length.National Science Foundation (U.S.) (Grant CNS-0915988)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238