Related papers: Upper and Lower Class Functions for Maximum Likeli…
We consider an M/M/Infinity service system in which an arriving customer is served by the first idle server in an infinite sequence S_1, S_2, ... of servers. We determine the first two terms in the asymptotic expansions of the moments of L…
We introduce the {\Delta}(i)/GI/1 queue, a new queueing model. In this model, customers from a given population independently sample a time to arrive from some given distribution F. Thus, the arrival times are an ordered statistics, and the…
Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump)…
In discrete time, customers arrive at random. Each waits until one of two servers is available; each thereafter departs at random. We seek the distribution of maximum line length of idle customers. In the context of an emergency room (for…
In this study, we consider multi-class multi-server asymmetric queueing systems consisting of $N$ queues on one side and $K$ servers on the other side, where jobs randomly arrive in queues at each time. The service rate of each job-server…
We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…
The infinite-server queueing models with homogeneous and non-homogeneous arrivals of customers and catastrophes are considered. The probability generating functions of joint distributions of numbers of busy servers and served customers, as…
We analyze worst-case convergence guarantees of first-order optimization methods over a function class extending that of smooth and convex functions. This class contains convex functions that admit a simple quadratic upper bound. Its study…
Accurate estimation of queuing delays is crucial for designing and optimizing communication networks, particularly in the context of Deterministic Networking (DetNet) scenarios. This study investigates the approximation of Internet queuing…
In this paper, we present a delay-optimal packet scheduler for processing the M2M uplink traffic at the M2M application server (AS). Due to the delay-heterogeneity in uplink traffic, we classify it broadly into delay-tolerant and…
Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression,…
The sensory traffic in Machine-to-Machine (M2M) communications has fairly heterogeneous service delay requirements. Therefore, we study the delay-performance of a heterogeneous M2M uplink from the sensors to a M2M application server (AS)…
We define a generalized likelihood function based on uncertainty measures and show that maximizing such a likelihood function for different measures induces different types of classifiers. In the probabilistic framework, we obtain…
Recently, Atar and Miyazawa [2] introduced a multi-level GI/G/1 queue with a finite number of levels, where both the arrival and service rates depend on the level corresponding to the current queue length. For this model, they proved that…
Let $x_{i,j}$, $1 \le i \le m$, $1 \le j \le n_i$, be observations from a doubly-indexed sequence $\{X_{i,j}\}$ of independent random variables (all of them discrete, or all of them absolutely continuous). Suppose that each $X_{i,j}$ has…
In this paper, we consider systems that can be modelled by $M \mid M \mid n$ queues with heterogeneous servers and non informed customers. Considering any two servers: we show that the probability that the fastest server is busy is smaller…
Distributions with a heavy tail are difficult to estimate. If the design of a scheduling policy is sensitive to the details of heavy tail distributions of the service times, an approximately optimal solution is difficult to obtain. This…
The application of the max-algebra to describe queueing systems by both linear scalar and vector equations is discussed. It is shown that these equations may be handled using ordinary algebraic manipulations. Examples of solving the…
In many applications, significant correlations between arrivals of load-generating events make the numerical evaluation of the load of a system a challenging problem. Here, we construct very accurate approximations of the workload…
The single server queue with multiple customer types and semi-Markovian service times, sometimes referred to as the $M/SM/1$ queue, has been well-studied since its introduction by Neuts in 1966. In this paper, we apply an extension of this…