No / Quality of Service (QoS) is of extreme importance in accommodating the increasingly diverse range of services and types of traffic in present day communication networks and delay is one of the most important QoS metrics. This paper presents a new approach for constraining queueing delay in a buffer to a specified level as the arrival rate changes with time. A discrete-time control algorithm is presented that operates on a buffer (queue) which incorporates a moveable threshold. An algorithm is developed that controls the delay by dynamically adjusting the threshold which, in turn, controls the arrival rate. The feasibility of the system is examined using both theoretical analysis and simulation.

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Scheduling policies adopted for statistical multiplexing should provide delay differentiation between different traffic classes, where each class represents an aggregate traffic of individual applications having same target-queueing-delay requirements. We propose scheduling to optimally balance weighted mean instanteneous queue lengths and later weighted mean cumulative queue lengths as an approach to delay differentiation, where the class weights are set inversely proportional to the respective products of target delays and packet arrival rates. In particular, we assume a discrete-time, two-class, single-server queueing model with unit service time per packet and provide mathematical frame-work throughout our work. For iid Bernoulli packet arrivals, using a step-wise cost-dominance analytical approach using instantaneous queue lengths alone, for a class of one-stage cost functions not necessarily convex, we find the structure of the total-cost optimal policies for a part of the state space. We then consider two particular one-stage cost functions for finding two scheduling policies that are total-cost optimal for the whole state-space. The policy for the absolute weighted difference cost function minimizes the stationary mean, and the policy for the weighted sum-of-square cost function minimizes the stationary second-order moment, of the absolute value of the weighted difference of queue lengths. For the case of weighted sum-of-square cost function, the ‘iid Bernoulli arrivals’ assumption can be relaxed to either ‘iid arrivals with general batch sizes’ or to ‘Markovian zero-one arrivals’ for all of the state space, but for the linear switching curve. We then show that the average cost, starting from any initial state, exists, and is finite for every stationary work-conserving policy for our choices of the one-stage cost-function. This is shown for arbitrary number of class queues and for any i.i.d. batch arrival processes with finite appropriate moments. We then use cumulative queue lengths information in the one-step cost function of the optimization formulation and obtain an optimal myopic policy with 3 stages to go for iid arrivals with general batch sizes. We show analytically that this policy achieves the given target delay ratio in the long run under finite buffer assumption, given that feasibility conditions are satisfied. We take recourse to numerical value iteration to show the existence of average-cost for this policy. Simulations with varied class-weights for Bernoulli arrivals and batch arrivals with Poisson batch sizes show that this policy achieves mean queueing delays closer to the respective target delays than the policy obtained earlier. We also note that the coefficients of variation of the queueing delays of both the classes using cumulative queue lengths are of the same order as those using instantaneous queue lengths. Moreover, the short-term behaviour of the optimal myopic policy using cumulative queue lengths is superior to the existing standard policy reported by Coffman and Mitrani by a factor in the range of 3 to 8. Though our policy performs marginally poorer compared to the value-iterated, sampled, and then stationarily employed policy, the later lacks any closed-form structure. We then modify the definition of the third state variable and look to directly balance weighted mean delays. We come up with another optimal myopic policy with 3 stages to go, following which the error in the ratio of mean delays decreases as the window-size, as opposed to the policy mentioned in the last paragraph, wherein the error decreases as the square-root of the window-size. We perform numerical value-iteration to show the existence of average-cost and study the performance by simulation. Performance of our policy is comparable with the value-iterated, sampled, and then stationarily employed policy, reported by Mallesh. We have then studied general inter-arrival time processes and obtained the optimal myopic policy for the Pareto inter-arrival process, in particular. We have supported with simulation that our policy fares similarly to the PAD policy, reported by Dovrolis et. al., which is primarily heuristic in nature. We then model the possible packet errors in the multiplexed channel by either a Bernoulli process, or a Markov modulated Bernoulli process with two possible channel states. We also consider two possible round-trip-time values for control information, namely zero and one-slot. The policies that are next-stage optimal (for zero round-trip-time), and two-stage optimal (for one-slot round-trip-time) are obtained. Simulations with varied class-weights for Bernoulli arrivals and batch arrivals with Poisson batch sizes show that these policies indeed achieve mean queueing delays very close to the respective target delays. We also obtain the structure for optimal policies with N = 2 + ⌈rtt⌉ stages-to-go for generic values of rtt, and which need not be multiple of time-slots.

Wireless technology has become an increasingly popular way to gain network access. Wireless networks are expected to provide efficient and reliable service and support a broad range of emerging applications, such as multimedia streaming and video conferencing. However, limited wireless spectrum together with interference and fading pose signi cant challenges for network designers. The novel technique of network coding has a significant potential for improving the throughput and reliability of wireless networks by taking advantage of the broadcast nature of wireless medium. Reverse carpooling is one of the main techniques used to realize the benefits of network coding in wireless networks. With reverse carpooling, two flows are traveling in opposite directions, sharing a common path. The network coding is performed in the intermediate (relay) nodes, which saves up to 50% of transmissions. In this thesis, we focus on the scheduling at the relay nodes in wireless networks with reverse carpooling. When two packets traveling in opposite directions are available at the relay node, the relay node combines them and broadcasts the resulting packet. This event is referred to as a coding opportunity. When only one packet is available, the relay node needs to decide whether to wait for future coding opportunities, or to transmit them without coding. Though the choice of holding packets exploits the positive aspects of network coding, without a proper policy in place that controls how long the packets should wait, it will have an adverse impact on delays and thus the overall network performance. Accordingly, our goal is to find an optimal control strategy that delicately balances the tradeoff between the number of transmissions and delays incurred by the packets. We also address the fundamental question of what local information we should keep track of and use in making the decision of of whether to transmit uncoded packet or wait for the next coding opportunity. The available information consists of queue length and time stamps indicating the arrival time of packets in the queue. We could also store history of all previous states and actions. However, using all this information makes the control very complex and so we try to find if the overhead in collecting waiting times and historical information is worth it. A major contribution of this thesis is a stochastic control framework that uses state information based on what can be observed and prescribes an optimal action. For that, we formulate and solve a stochastic dynamic program with the objective of minimizing the long run average cost per unit time incurred due to transmissions and delays. Subsequently, we show that a stationary policy based on queue lengths is optimal, and the optimal policy is of threshold-type. Then, we describe a non-linear optimization procedure to obtain the optimal thresholds. Further, we substantiate our analytical ndings by performing numerical experiments under varied settings. We compare systems that use only queue length with those where more information is available, and we show that optimal control that uses only the queue length is as good as any optimal control that relies on knowing the entire history.

Traditionally the Internet is used for the following applications: FTP, e-mail and Web traffic. However in the recent years the Internet is increasingly supporting emerging applications such as IP telephony, video conferencing and online games. These new applications have different requirements in terms of throughput and delay than traditional applications. For example, interactive multimedia applications, unlike traditional applications, have more strict delay constraints and less strict loss constraints. Unfortunately, the current Internet offers only a best-effort service to all applications without any consideration to the applications specific requirements. In this thesis three existing Active Queue Management (AQM) mechanisms are modified by incorporating into these a control function to condition routers for better Quality of Service (QoS). Specifically, delay is considered as the key QoS metric as it is the most important metric for real-time multimedia applications. The first modified mechanism is Drop Tail (DT), which is a simple mechanism in comparison with most AQM schemes. A dynamic threshold has been added to DT in order to maintain packet queueing delay at a specified value. The modified mechanism is referred to as Adaptive Drop Tail (ADT). The second mechanism considered is Early Random Drop (ERD) and, iii in a similar way to ADT, a dynamic threshold has been used to keep the delay at a required value, the main difference being that packets are now dropped probabilistically before the queue reaches full capacity. This mechanism is referred to as Adaptive Early Random Drop (AERD). The final mechanism considered is motivated by the well known Random Early Detection AQM mechanism and is effectively a multi-threshold version of AERD in which packets are dropped with a linear function between the two thresholds and the second threshold is moveable in order to change the slope of the dropping function. This mechanism is called Multi Threshold Adaptive Early Random Drop (MTAERD) and is used in a similar way to the other mechanisms to maintain delay around a specified level. The main focus with all the mechanisms is on queueing delay, which is a significant component of end-to-end delay, and also on reducing the jitter (delay variation) A control algorithm is developed using an analytical model that specifies the delay as a function of the queue threshold position and this function has been used in a simulation to adjust the threshold to an effective value to maintain the delay around a specified value as the packet arrival rate changes over time. iv A two state Markov Modulated Poisson Process is used as the arrival process to each of the three systems to introduce burstiness and correlation of the packet inter-arrival times and to present sudden changes in the arrival process as might be encountered when TCP is used as the transport protocol and step changes the size of its congestion window. In the investigations it is assumed the traffic source is a mixture of TCP and UDP traffic and that the mechanisms conserved apply to the TCP based data. It is also assumed that this consists of the majority proportion of the total traffic so that the control mechanisms have a significant effect on controlling the overall delay. The three mechanisms are evaluated using a Java framework and results are presented showing the amount of improvement in QoS that can be achieved by the mechanisms over their non-adaptive counterparts. The mechanisms are also compared with each other and conclusions drawn.

We consider a congestion control problem in computer networks. The problem is posed as an optimal control problem and reduced to a problem of finding solutions to delay differential equations. Systems involving time delays in the dynamics are actually very difficult to model and therefore very difficult to solve. We consider three approaches in our congestion control problem: an elastic queue approach leading to an optimal control problem with a state–dependent delay differential equation; three approaches in flow models (also leading to systems containing delay differential equations), precisely the dual control approach, the primal–dual control approach and the control approach based on queueing delay. The elastic queue approach is not explored due to the lack of software good enough to solve optimal control problems involving delay differential equations. In flow models, we consider the standard case, that is where the feedback from sources to links is exact and the network behaves perfectly well (without any unexpected event). We also consider some non–standard cases such as the case where this feedback contains errors (for example overestimation, underestimation or noise), and the case where one link breaks in the network. We numerically solve the delay differential equations obtained and use the results we get to determine all the considered dynamics in the network. This is followed by an analysis of the results. We also explore the stability of some simple cases in the dual control approach, with weaker conditions on some network parameters, and discuss some fairness conditions in some simple cases in all the flow model approaches. Non–standard cases are also solved numerically and the results can be compared with those obtained in the standard case.

Traditionally the Internet is used for the following applications: FTP, e-mail and Web traffic. However in the recent years the Internet is increasingly supporting emerging applications such as IP telephony, video conferencing and online games. These new applications have different requirements in terms of throughput and delay than traditional applications. For example, interactive multimedia applications, unlike traditional applications, have more strict delay constraints and less strict loss constraints. Unfortunately, the current Internet offers only a best-effort service to all applications without any consideration to the applications specific requirements. In this thesis three existing Active Queue Management (AQM) mechanisms are modified by incorporating into these a control function to condition routers for better Quality of Service (QoS). Specifically, delay is considered as the key QoS metric as it is the most important metric for real-time multimedia applications. The first modified mechanism is Drop Tail (DT), which is a simple mechanism in comparison with most AQM schemes. A dynamic threshold has been added to DT in order to maintain packet queueing delay at a specified value. The modified mechanism is referred to as Adaptive Drop Tail (ADT). The second mechanism considered is Early Random Drop (ERD) and, iii in a similar way to ADT, a dynamic threshold has been used to keep the delay at a required value, the main difference being that packets are now dropped probabilistically before the queue reaches full capacity. This mechanism is referred to as Adaptive Early Random Drop (AERD). The final mechanism considered is motivated by the well known Random Early Detection AQM mechanism and is effectively a multi-threshold version of AERD in which packets are dropped with a linear function between the two thresholds and the second threshold is moveable in order to change the slope of the dropping function. This mechanism is called Multi Threshold Adaptive Early Random Drop (MTAERD) and is used in a similar way to the other mechanisms to maintain delay around a specified level. The main focus with all the mechanisms is on queueing delay, which is a significant component of end-to-end delay, and also on reducing the jitter (delay variation) A control algorithm is developed using an analytical model that specifies the delay as a function of the queue threshold position and this function has been used in a simulation to adjust the threshold to an effective value to maintain the delay around a specified value as the packet arrival rate changes over time. iv A two state Markov Modulated Poisson Process is used as the arrival process to each of the three systems to introduce burstiness and correlation of the packet inter-arrival times and to present sudden changes in the arrival process as might be encountered when TCP is used as the transport protocol and step changes the size of its congestion window. In the investigations it is assumed the traffic source is a mixture of TCP and UDP traffic and that the mechanisms conserved apply to the TCP based data. It is also assumed that this consists of the majority proportion of the total traffic so that the control mechanisms have a significant effect on controlling the overall delay. The three mechanisms are evaluated using a Java framework and results are presented showing the amount of improvement in QoS that can be achieved by the mechanisms over their non-adaptive counterparts. The mechanisms are also compared with each other and conclusions drawn.

A scheduling algorithm has the primary role in implementing the quality of service guaranteed to each flow by managing buffer space and selecting which packet to send next with a fair share of network. In this thesis, some scheduling algorithms for packet switching networks are studied. For evaluating their delay, jitter and throughput performances, a discrete event simulator has been developed. It has been seen that fair scheduling provides, fair allocation of bandwidth, lower delay for sources using less than their full share of bandwidth and protection from ill-behaved resources.

Peer to peer networks are becoming increasingly popular among Internet users as the downloading peers share the storage and upload bandwidth load of the system. This makes it possible for a large number of users to share a data file available at a server without the server upload bandwidth becoming a bottleneck. The P2P technology is being widely used not only for file sharing but also for video on demand, live streaming and IPTV. The delay deadlines are more stringent in live streaming and IPTV than those in file sharing as the traffic is real time. The performance perceived by a user depends upon whether the video stream is being downloaded at the streaming rate. Coolstreaming is the first large scale P2P IPTV system. We model the multi-channel Coolstreaming system via an open queueing network. The peer dynamics at a channel is modelled by a closed queueing network working at a faster rate. We compute the expected number of substreams in the overlay of New Coolstreaming which are not being received at the proper rate. The computation of the Markov chain with a very large state space is handled using the two time scale decomposition. Further we characterize the end to end delay encountered by a video stream originating from the server and received at a user of New Coolstreaming. Three factors contribute towards the delay. The first factor is the mean path length in terms of overlay hops of the partnership graph. The second factor is the mean number of routers between any two overlay peers in the network layer and the third factor is the queueing delay at a router in the Internet. The mean shortest path length in terms of overlay peers in the New Coolstreaming graph is shown to be O(logn)where nis the number of peers in the overlay. This is done by modelling the overlay by a random graph. The mean shortest path in terms of routers in the Internet’s router level topology is seen to be at most O(logNI)where NIis the number of routers in the Internet. We also discuss a method by which we can get the mean delay at a router in the Internet. Thus, the mean end to end delay in New Coolstreaming is shown to be upper bounded by O(lognlogNIE[W])where E[W]is the mean delay at a router in the Internet.