The paper deals with Age of Information (AoI) in a network of multiple sources and parallel queues with buffering capabilities, preemption in service and losses in served packets. The queues do not communicate between each other and the packets are dispatched through the queues according to a predefined probabilistic routing. By making use of the Stochastic Hybrid System (SHS) method, we provide a derivation of the average AoI of a system of two parallel queues (with and without buffer capabilities) and compare the results with those of a single queue. We show that known results of packets delay in Queuing Theory do not hold for the AoI. Unfortunately, the complexity of computing the average AoI using the SHS method increases highly with the number of queues. We therefore provide an upper bound of the average AoI in a system of an arbitrary number of M/M/1/(N+1) queues and show its tightness in various regimes. This upper bound allows providing a tight approximation of the average AoI with a very low complexity. We then provide a game framework that allows each source to determine its best probabilistic routing decision. By using Mean Field Games, we provide an analysis of the routing game framework, propose an efficient iterative method to find the routing decision of each source and prove its convergence to the desired equilibrium.
We consider the age-of-information in a multi-class $M/G/1$ queueing system, where each class generates packets containing status information. Age of information is a relatively new metric that measures the amount of time that elapsed between status updates, thus accounting for both the queueing delay and the delay between packet generation. This gives rise to a tradeoff between frequency of status updates, and queueing delay. In this paper, we study this tradeoff in a system with heterogenous users modeled as a multi-class $M/G/1$ queue. To this end, we derive the exact peak age-of-Informatio…
We analyze opportunistic schemes for transmission scheduling from one of $n$ homogeneous queues whose channel states fluctuate independently. Considered schemes consist of the LCQ policy, which transmits from a longest connected queue in the entire system, and its low-complexity variants that transmit from a longest queue within a randomly chosen subset of connected queues. A Markovian model is studied where mean packet transmission time is $n^{-1}$ and packet arrival rate is $λ<1$ per queue. Transient and equilibrium distributions of queue occupancies are obtained in the limit as the system s…
Most input buffered packet switches internally segment variable-length packets into fixed-length cells. The last cell in a segmented packet will contain overhead bytes if the packet length is not evenly divisible by the cell length. Switch speed-up is used to compensate for this overhead. In this paper, we develop an analytical model of a single-server queue where an input stream of packets is segmented into cells for service. Analytical models are developed for M/M/1, M/H2/1, and M/E2/1 queues with a discretized (or quantized) service time. These models and simulation using real packet traces…
This paper presents a performance analysis for the bandwidth allocation in IEEE 802.16 broadband wireless access (BWA) networks considering the packet-level quality-of-service (QoS) constraints. Adaptive Modulation and Coding (AMC) rate based on IEEE 802.16 standard is used to adjust the transmission rate adaptively in each frame time according to channel quality in order to obtain multiuser diversity gain. To model the arrival process and the traffic source we use the Batch Markov Arrival Process (BMAP), which enables more realistic and more accurate traffic modelling. We determine analytical…
Analytical models for IEEE 802.11-based WLANs are invariably based on approximations, such as the well-known \textit{decoupling approximation} proposed by Bianchi for modeling single cell WLANs consisting of saturated nodes. In this paper, we provide a new approach to model the situation when the nodes are not saturated. We study a State Dependent Attempt Rate (SDAR) approximation to model $M$ queues (one queue per node) served by the CSMA/CA protocol as standardized in the IEEE 802.11 DCF MAC protocol. The approximation is that, when $n$ of the $M$ queues are non-empty, the transmission attem…
We show how to calculate the Age of Information in an overtake-free network of quasi-reversible queues, with exponential exogenous interarrivals of multiple classes of update packets and exponential service times at all nodes. Results are provided for any number of M/M/1 First-Come-First-Served (FCFS) queues in tandem, and for a network with two classes of update packets, entering through different queues in the network and exiting through the same queue. The main takeaway is that in a network with different classes of update packets, individual classes roughly preserve the ages they would ach…
Motivated by medium access control for resource-challenged wireless Internet of Things (IoT), we consider the problem of queue scheduling with reduced queue state information. In particular, we consider a time-slotted scheduling model with $N$ sensor nodes, with pair-wise dependence, such that Nodes $i$ and $i + 1,~0 < i < N$ cannot transmit together. We develop new throughput-optimal scheduling policies requiring only the empty-nonempty state of each queue that we term Queue Nonemptiness-Based (QNB) policies. We propose a Policy Splicing technique to combine scheduling policies for small netw…
In this paper we consider a real time queuing system with rewards and deadlines. We assume that packet processing time is known upon arrival, as is the case in communication networks. This assumption allows us to demonstrate that the well known Earliest-Deadline-First policy performance can be improved. We then propose a scheduling policy that provides excellent results for packets with rewards and deadlines. We prove that the policy is optimal under deterministic service time and binomial reward distribution. In the more general case we prove that the policy processes the maximal number of pa…
As one of the most popular south-bound protocol of software-defined networking(SDN), OpenFlow decouples the network control from forwarding devices. It offers flexible and scalable functionality for networks. These advantages may cause performance issues since there are performance penalties in terms of packet processing speed. It is important to understand the performance of OpenFlow switches and controllers for its deployments. In this paper we model the packet processing time of OpenFlow switches and controllers. We mainly analyze how the probability of packet-in messages impacts the perfor…
MIT Lincoln Laboratory（麻省理工学院林肯实验室）；MIT Laboratory for Information and Decision Systems（麻省理工学院信息与决策系统实验室）
We consider a system consisting of a single transmitter/receiver pair and $N$ channels over which they may communicate. Packets randomly arrive to the transmitter's queue and wait to be successfully sent to the receiver. The transmitter may attempt a frame transmission on one channel at a time, where each frame includes a packet if one is in the queue. For each channel, an attempted transmission is successful with an unknown probability. The transmitter's objective is to quickly identify the best channel to minimize the number of packets in the queue over $T$ time slots. To analyze system perf…
We consider a fading point-to-point link with packets arriving randomly at rate $λ$ per slot to the transmitter queue. We assume that the transmitter can control the number of packets served in a slot by varying the transmit power for the slot. We restrict to transmitter scheduling policies that are monotone and stationary, i.e., the number of packets served is a non-decreasing function of the queue length at the beginning of the slot for every slot fade state. For such policies, we obtain asymptotic lower bounds for the minimum average delay of the packets, when average transmitter power is a…
Scheduling is a critical and challenging resource allocation mechanism for multihop wireless networks. It is well known that scheduling schemes that favor links with larger queue length can achieve high throughput performance. However, these queue-length-based schemes could potentially suffer from large (even infinite) packet delays due to the well-known last packet problem, whereby packets belonging to some flows may be excessively delayed due to lack of subsequent packet arrivals. Delay-based schemes have the potential to resolve this last packet problem by scheduling the link based on the d…
In this thesis, we study the optimal tradeoff of average delay, average service cost, and average utility for single server queueing models, with and without admission control. The continuous time and discrete time queueing models that we consider are motivated by cross-layer models for noisy point-to-point links, with random packet arrivals. We study the above tradeoff problem for a class of admissible policies, which are monotone and stationary and obtain an asymptotic characterization of the minimum average delay as a function of the average service cost and average utility constraints.
We consider the fundamental problem of managing a bounded size queue buffer where traffic consists of packets of varying size, where each packet requires several rounds of processing before it can be transmitted from the queue buffer. The goal in such an environment is to maximize the overall size of packets that are successfully transmitted. This model is motivated by the ever-growing ubiquity of network processors architectures, which must deal with heterogeneously-sized traffic, with heterogeneous processing requirements. Our work addresses the tension between two conflicting algorithmic ap…
We consider the peak age-of-information (PAoI) in an M/M/1 queueing system with packet delivery error, i.e., update packets can get lost during transmissions to their destination. We focus on two types of policies, one is to adopt Last-Come-First-Served (LCFS) scheduling, and the other is to utilize retransmissions, i.e., keep transmitting the most recent packet. Both policies can effectively avoid the queueing delay of a busy channel and ensure a small PAoI. Exact PAoI expressions under both policies with different error probabilities are derived, including First-Come-First-Served (FCFS), LCF…
On the Age of Status Updates in Unreliable Multi-Source M/G/1 Queueing Systems
PSG College of Technology（PSG理工学院）；University of Alberta（阿尔伯塔大学）；Nazarbayev University（纳扎尔巴耶夫大学）；Institute for Research in Fundamental Sciences（基础科学研究所）；University of Tehran（德黑兰大学）；Jinan University（暨南大学）
In network quality of service provisioning, premium services generally require to keep a very small loss probability, which is infeasible to measure directly. The proposed virtual queue scheme estimates the small packet loss probability of a real queueing system by measuring queue statistics in a set of separate virtual queues. A novel scaling property between the real queue and the virtual queues is deduced on the basis of the maximum variance asymptotic (MVA) theory. The new scheme retains the high accuracy and wide applicability of the MVA method for aggregated traffic while avoiding the hi…
