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.     

Analysis of a discrete-time preemptive resume priority buffer

In this paper, we analyze a discrete-time preemptive resume priority queue. We consider two classes of customers which have to be served, where customers of one class have preemptive resume priority over customers of the other. Both classes contain customers with generally distributed service times. We show that the use of probability generating functions is beneficial for analyzing the system contents and customer delays of both classes. It is shown (theoretically as well as by some practical procedures) how moments and approximate tail probabilities of system contents and customer delays are calculated. The influence of the priority scheduling discipline and the service time distributions on the performance measures is shown by some numerical examples.     

A multi-class discrete-time queueing system under the FCFS service discipline

The problem with the FCFS server discipline in discrete-time queueing systems is that it doesn’t actually determine what happens if multiple customers enter the system at the same time, which in the discrete-time paradigm translates into ‘during the same time-slot’. In other words, it doesn’t specify in which order such customers are served. When we consider multiple types of customers, each requiring different service time distributions, the precise order of service even starts to affect quantities such as queue content and delays of arbitrary customers, so specifying this order will be prime. In this paper we study a multi-class discrete-time queueing system with a general independent arrival process and generally distributed service times. The service discipline is FCFS and customers entering during the same time-slot are served in random order. It will be our goal to search for the steady-state distribution of queue content and delays of certain types of customers. If one thinks of the time-slot as a continuous but bounded time period, the random order of service is equivalent to FCFS if different customers have different arrival epochs within this time-slot and if the arrival epochs are independent of customer class. For this reason we propose two distinct ways of analysing; one utilizing permutations, the other considering a slot as a bounded continuous time frame.     

A detailed note on the finite-buffer queueing system with correlated batch-arrivals and batch-size-/phase-dependent bulk-service

4OR - This paper analyzes a finite-buffer queueing system, where customers arrive in batches and the accepted customers are served in batches by a single server. The service is assumed to be...     

Delay analysis of a discrete-time multiclass slot-bound priority system

This paper introduces a new priority mechanism in discrete-time queueing systems that compromises between first-come-first-served (FCFS) and head-of-line priority. In this scheduling discipline—which we dubbed slot-bound priority—customers of different priority classes entering the system during the same time-slot are served in order of their respective priority class. Customers entering during different slots are served on a FCFS basis. In this paper we study the delay in an N-class discrete-time queueing system under slot-bound priority. General independent arrivals and class-specific general service time distributions are assumed. Expressions for the probability generating function of the delay of a random type-j customer are derived, from which the respective moments are easily obtained. The tail behaviour of these distributions is analyzed as well, and some numerical examples show the effect slot-bound priority can have on the performance measures.     

Calculation of delay characteristics for multiserver queues with constant service times

We consider a discrete-time infinite-capacity queueing system with a general uncorrelated arrival process, constant-length service times of multiple slots, multiple servers and a first-come-first-served queueing discipline. Under the assumption that the queueing system can reach a steady state, we first establish a relationship between the steady-state probability distributions of the system content and the customer delay. Next, by means of this relationship, an explicit expression for the probability generating function of the customer delay is obtained from the known generating function of the system content, derived in previous work. In addition, several characteristics of the customer delay, namely the mean value, the variance and the tail distribution of the delay, are derived through some mathematical manipulations. The analysis is illustrated by means of some numerical examples.     

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.     

Analyzing the discrete-timeG (G)/Geo/1 queue using complex contour integration

In this paper, a discrete-time single-server queueing system with an infinite waiting room, referred to as theG ^(G)/Geo/1 model, i.e., a system with general interarrival-time distribution, general arrival bulk-size distribution and geometrical service times, is studied. A method of analysis based on integration along contours in the complex plane is presented. Using this technique, analytical expressions are obtained for the probability generating functions of the system contents at various observation epochs and of the delay and waiting time of an arbitrary customer, assuming a first-come-first-served queueing discipline, under the single restriction that the probability generating function for the interarrival-time distribution be rational. Furthermore, treating several special cases we rediscover a number of well-known results, such as Hunter's result for theG/Geo/1 model. Finally, as an illustration of the generality of the analysis, it is applied to the derivation of the waiting time and the delay of the more generalG ^(G)/G/1 model and the system contents of a multi-server buffer-system with independent arrivals and random output interruptions.Both authors wish to thank the Belgian National Fund for Scientific Research (NFWO) for support of this work.     

Spectroscopic Investigations of Polymer Nanocomposites

The addition of an inorganic component to polymers leads to improvements in various physical and mechanical properties. Various examples on filled elastomeric networks will show that a mechanical characterization can be nicely combined with a spectroscopic investigation for a better understanding of the properties of the composite materials.