End-to-end delay is a critical attribute of quality of service (QoS) in application domains such as cloud computing and computer networks. This metric is particularly important in tandem service systems, where the end-to-end service is provided through a chain of services. Service-rate control is a common mechanism for providing QoS guarantees in service systems. In this paper, we introduce a reinforcement learning-based (RL-based) service-rate controller that provides probabilistic upper-bounds on the end-to-end delay of the system, while preventing the overuse of service resources. In order to have a general framework, we use queueing theory to model the service systems. However, we adopt an RL-based approach to avoid the limitations of queueing-theoretic methods. In particular, we use Deep Deterministic Policy Gradient (DDPG) to learn the service rates (action) as a function of the queue lengths (state) in tandem service systems. In contrast to existing RL-based methods that quantify their performance by the achieved overall reward, which could be hard to interpret or even misleading, our proposed controller provides explicit probabilistic guarantees on the end-to-end delay of the system. The evaluations are presented for a tandem queueing system with non-exponential inter-arrival and service times, the results of which validate our controller's capability in meeting QoS constraints.

Ensuring quality of service (QoS) guarantees in service systems is a challenging task, particularly when the system is composed of more fine-grained services, such as service function chains. An important QoS metric in service systems is the end-to-end delay, which becomes even more important in delay-sensitive applications, where the jobs must be completed within a time deadline. Admission control is one way of providing end-to-end delay guarantee, where the controller accepts a job only if it has a high probability of meeting the deadline. In this paper, we propose a reinforcement learning-based admission controller that guarantees a probabilistic upper-bound on the end-to-end delay of the service system, while minimizes the probability of unnecessary rejections. Our controller only uses the queue length information of the network and requires no knowledge about the network topology or system parameters. Since long-term performance metrics are of great importance in service systems, we take an average-reward reinforcement learning approach, which is well suited to infinite horizon problems. Our evaluations verify that the proposed RL-based admission controller is capable of providing probabilistic bounds on the end-to-end delay of the network, without using system model information.

Ensuring the conformance of a service system's end-to-end delay to service level agreement (SLA) constraints is a challenging task that requires statistical measures beyond the average delay. In this paper, we study the real-time prediction of the end-to-end delay distribution in systems with composite services such as service function chains. In order to have a general framework, we use queueing theory to model service systems, while also adopting a statistical learning approach to avoid the limitations of queueing-theoretic methods such as stationarity assumptions or other approximations that are often used to make the analysis mathematically tractable. Specifically, we use deep mixture density networks (MDN) to predict the end-to-end distribution of the delay given the network's state. As a result, our method is sufficiently general to be applied in different contexts and applications. Our evaluations show a good match between the learned distributions and the simulations, which suggest that the proposed method is a good candidate for providing probabilistic bounds on the end-to-end delay of more complex systems where simulations or theoretical methods are not applicable.

Motivated by interest in providing more efficient services in customer service systems, we use statistical learning methods and delay history information to predict the conditional distribution of the customers' waiting times in queueing systems. From the predicted distributions, descriptive statistics of the system such as mean, variance and percentiles of the waiting times can be obtained, which can be used for delay announcements, SLA conformance and better system management. We model the distributions by mixtures of Gaussians, parameters of which can be estimated using Mixture Density Networks. We use the extensions of the Lindley's equation for multi-server queues to generate our datasets. The evaluations show that exploiting more delay history information can result in much more accurate predictions under realistic time-varying arrival assumptions.