43 research outputs found
Estimating multiclass service demand distributions using Markovian arrival processes
Building performance models for software services in DevOps is costly and error-prone. Accurate service demand distribution estimation is critical to precisely modeling queueing behaviors and performance prediction. However, current estimation methods focus on capturing the mean service demand, disregarding higher-order moments of the distribution that still can largely affect prediction accuracy. To address this limitation, we propose to estimate higher moments of the service demand distribution for a microservice from monitoring traces. We first generate a closed queueing model to abstract software performance and use it to model the departure process of requests completed by the software service as a Markovian arrival process. This allows formulating the estimation of service demand into an optimization problem, which aims to find the first multiple moments of the service demand distribution that maximize the likelihood of the MAP using generated the measured inter-departure times. We then estimate the service demand distribution for different classes of service with a maximum likelihood algorithm and novel heuristics to mitigate the computational cost of the optimization process for scalability. We apply our method to real traces from a microservice-based application and demonstrate that its estimations lead to greater prediction accuracy than exponential distributions assumed in traditional service demand estimation approaches for software services
Stability of queueing-inventory systems with different priorities
We study a production-inventory system with two customer classes with
different priorities which are admitted to the system following a flexible
admission control scheme. The inventory management is according to a base stock
policy and arriving demand which finds the inventory depleted is lost (lost
sales). We analyse the global balance equations of the associated Markov
process and derive structural properties of the steady state distribution which
provide insights into the equilibrium behaviour of the system. We derive a
sufficient condition for ergodicity using the Foster-Lyapunov stability
criterion. For a special case we show that the condition is necessary as well
Analysis of Stochastic Models through Multi-Layer Markov Modulated Fluid Flow Processes
This thesis is concerned with the multi-layer Markov modulated fluid flow (MMFF) processes and their applications to queueing systems with customer abandonment.
For the multi-layer MMFF processes, we review and refine the theory on the joint distribution of the multi-layer MMFF processes and develop an easy to implement algorithm to calculate the joint distribution. Then, we apply the theory to three quite general queueing systems with customer abandonment to show the applicability of this approach and obtain a variety of queueing quantities, such as the customer abandonment probabilities, waiting times distributions and mean queue lengths.
The first application is the MAP/PH/K+GI queue. The MMFF approach and the count-server-for-phase (CSFP) method are combined to analyze this multi-server queueing system with a moderately large number of servers. An efficient and easy-to-implement algorithm is developed for the performance evaluation of the MAP/PH/K +GI queueing model. Some of the queueing quantities such as waiting time distributions of the customers abandoning the queue at the head of the waiting queue are difficult to derive through other methods.
Then the double-sided queues with marked Markovian arrival processes (MMAP) and abandonment are studied. Multiple types of inputs and finite discrete abandonment times make this queueing model fairly general. Three age processes related to the inputs are defined and then converted into a multi-layer MMFF process. A number of aggregate queueing quantities and quantities for individual types of inputs are obtained by the MMFF approach, which can be useful for practitioners to design stochastic systems such as ride-hailing platforms and organ transplantation systems.
The last queueing model is the double-sided queues with batch Markovian arrival processes (BMAP) and abandonment, which arise in various stochastic systems such as perishable inventory systems and financial markets. Customers arrive at the system with a batch of orders to be matched by counterparts. The abandonment time of a customer depends on the batch size and the position in the queue of the customer. Similar to the previous double-sided queueing model, a multi-layer MMFF process related to some age processes is constructed. A number of queueing quantities including matching rates, fill rates, sojourn times and queue length for both sides of the system are derived. This queueing model is used to analyze a vaccine inventory system as a case study in the thesis.
Overall, this thesis studies the joint stationary distribution of the multi-layer MMFF processes and shows the power of this approach in dealing with complex queueing systems. Four algorithms are presented to help practitioners to design stochastic systems and researchers do numerical experiments
Stochastic Processes with Applications
Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included