Packet loss characteristics for <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/1/<Emphasis Type="Italic">N</Emphasis> queueing systems

In this contribution we investigate higher-order loss characteristics for M/G/1/N queueing systems. We focus on the lengths of the loss and non-loss periods as well as on the number of arrivals during these periods. For the analysis, we extend the Markovian state of the queueing system with the time and number of admitted arrivals since the instant where the last loss occurred. By combining transform and matrix techniques, expressions for the various moments of these loss characteristics are found. The approach also yields expressions for the loss probability and the conditional loss probability. Some numerical examples then illustrate our results.     

Queueing systems with different types of server interruptions

We consider a queueing system with disruptive and non-disruptive server interruptions. Both disruptive and non-disruptive interruptions may start when there is a customer in service. The customer repeats its service after a disruptive interruption, and continues its service after a non-disruptive interruption. Using a transform approach, we obtain various performance measures such as the moments of the queue content and waiting times. We illustrate our approach by means of some numerical examples.     

The discrete-time preemptive repeat identical priority queue

Priority queueing systems come natural when customers with diversified delay requirements have to wait to get service. The customers that cannot tolerate but small delays get service priority over customers which are less delay-sensitive. In this contribution, we analyze a discrete-time two-class preemptive repeat identical priority queue with infinite buffer space and generally distributed service times. Newly arriving high-priority customers interrupt the on-going service of a low-priority customer. After all high-priority customers have left the system, the interrupted service of the low-priority customer has to be repeated completely. By means of a probability generating functions approach, we analyze the system content and the delay of both types of customers. Performance measures (such as means and variances) are calculated and the impact of the priority scheduling is discussed by means of some numerical examples.     

Analytic approximations of queues with lightly- and heavily-correlated autoregressive service times

We consider a single-server queueing system. The arrival process is modelled as a Poisson process while the service times of the consecutive customers constitute a sequence of autoregressive random variables. Our interest into autoregressive service times comes from the need to capture temporal correlation of the channel conditions on wireless network links. If these fluctuations are slow in comparison with the transmission times of the packets, transmission times of consecutive packets are correlated. Such correlation needs to be taken into account for an accurate performance assessment. By means of a transform approach, we obtain a functional equation for the joint transform of the queue content and the current service time at departure epochs in steady state. To the best of our knowledge, this functional equation cannot be solved by exact mathematical techniques, despite its simplicity. However, by means of a Taylor series expansion in the parameter of the autoregressive process, a “light-correlation” approximation is obtained for performance measures such as moments of the queue content and packet delay. We illustrate our approach by some numerical examples, thereby assessing the accuracy of our approximations by simulation. For the heavy correlation case, we give differential equation approximations based on the time-scale separation technique, and present numerical examples in support of this approximation.     

The value of information in energy harvesting sensor networks

We study optimal data collection in energy harvesting sensor networks. The sensed data-stream constitutes a sequence of stationary ergodic random variables and, assuming that timely data is valued more, the value of the data is discounted over time such that frequent collection is required to avoid a loss in value. However, unlimited data collection is constrained by both the cost of data collection and the availability of energy.     

Gated polling with stationary ergodic walking times, Markovian routing and random feedback

We investigate a gated polling system with semi-linear feedback and Markovian routing. We thereby relax the classical independence assumption on the walking times; the walking times constitute a sequence of stationary ergodic random variables. It is shown that the dynamics of this polling system can be described by semi-linear stochastic recursive equations in a Markovian environment. We obtain expressions for the first and second order moments of the workload and queue content at polling instants and for the mean queue content and workload at random instants.     

Analysis of a Discrete-Time Queueing System with Timed Vacations

We consider a discrete-time GI-G-1 queueing system with server vacations. Vacations occur whenever the queue becomes empty or whenever a timer expires. When the timer expires one of the following four actions are considered: the server completes transmission of the present packet before leaving for a vacation, the service immediately leaves for a vacation and the interrupted packet's service is either continued, repeated or resampled and repeated after the vacation. Using a probability generating functions approach, we derive various performance measures such as moments of the buffer contents at various time epochs in equilibrium and moments of the packet delay in equilibrium. By means of an example, we then compare the operation modes under consideration.     

Calculation of output characteristics of a priority queue through a busy period analysis

In this paper, we analyze some output characteristics of a discrete-time two-class priority queue by means of probability generating functions. Therefore, we construct a Markov chain which – after analysis – provides a.o. the probability generating functions of the lengths of the busy periods of both classes. It is furthermore shown how performance measures, related to the output process, are calculated from these functions. The queueing model is kept fairly simple to explain the method of analysis of the busy periods and the output characteristics of priority queues as clearly as possible.     

Computationally efficient evaluation of appointment schedules in health care

We consider the problem of evaluating and constructing appointment schedules for patients in a health care facility where a single physician treats patients in a consecutive manner, as is common for general practitioners, clinics and for outpatients in hospitals. Specifically, given a fixed-length session during which a physician sees K patients, each patient has to be given an appointment time during this session in advance. Optimising a schedule with respect to patient waiting times, physician idle times, session overtime, etc. usually requires a heuristic search method involving a huge number of repeated schedule evaluations. Hence, our aim is to obtain accurate predictions at very low computational cost. This is achieved by (1) using Lindley’s recursion to allow for explicit expressions and (2) choosing a discrete-time (slotted) setting to make those expressions easy to compute. We assume general, possibly distinct, distributions for the patients’ consultation times, which allows to account for multiple treatment types, emergencies and patient no-shows. The moments of waiting and idle times are obtained and the computational complexity of the algorithm is discussed. Additionally, we calculate the schedule’s performance in between appointments in order to assist a sequential scheduling strategy.