In this work we introduce a novel queueing model with two classes of users in which, instead of accessing a resource, users wait in the system to match with a candidate from the other class. The users are selective and the matchings occur probabilistically. This new model is useful for analysing the traffic in web portals that match people who provide a service with people who demand the same service, e.g. employment portals, matrimonial and dating sites and rental portals. We first provide a Markov chain model for these systems and derive the probability distribution of the number of matches up to some finite time given the number of arrivals. We then prove that if no control mechanism is employed these systems are unstable for any set of parameters. We suggest four different classes of control policies to assure stability and conduct analysis on performance measures under the control policies. Contrary to the intuition that the rejection rate should decrease as the users become more likely to be matched, we show that for certain control policies the rejection rate is insensitive to the matching probability. Even more surprisingly, we show that for reasonable policies the rejection rate may be an increasing function of the matching probability. We also prove insensitivity results related to the average queue lengths and waiting times. Further, to gain more insight into the behaviour of probabilistic matching systems, we propose approximation methods based on fluid and diffusion limits using different scalings. We analyse the basic properties of these approximations and show that some performance measures are insensitive to the matching probability agreeing with the results found by the exact analysis. Finally we study the optimal control and revenue management for the systems with the objective of profit maximization. We formulate mathematical models for both unobservable and observable systems. For an unobservable system we suggest a deterministic optimal control, while for an observable system we develop an optimal myopic state dependent pricing.

The practice of obtaining blood as part of the placement of a new peripheral venous access device (p-VAD) is a frequent practice in the emergency department (ED). Of the concerns related to this practice is the possibility of laboratory specimen rejection due to p-VAD catheter size, use of the wrong collection device, and the absence of a standardized collection process. The objective of this study, therefore, was to examine the effect of the use of evidence-based venipuncture and p-VAD blood collection protocols on the rejection rate of blood specimens drawn by staff in the adult areas of an urban academic medical center ED. A convenience sample of 28 ED nurses and 39 ED technicians (51.94% of all eligible ED employees) consented to using these evidence based protocols when they collected blood from adult ED patients. Blood specimen rejections rates were measured for four consecutive weeks prior to and at weeks 1-4, 5-8, 9-12, and 1-12 after the evidence-based blood collection practices training intervention. Laboratory analysis of all specimens was automated with rejection results provided in the form of computerized reports. There was a significant decrease in the 12-week rejection rates for two of the three ED adult care areas, with the overall ED adult area rejection rate significantly decreased from 3.19% to 2.38% (X2at Df1, p < .05). The most common reasons for rejection were hemolysis (65.39%) and clotting (10.68%) followed by specimen mis-labeling, tube missing, insufficient quantity for testing, incorrect packaging, specimen contamination or dilution, and label missing, Though the use of theses evidence based blood collection protocols significantly decreased the overall rejection rate, the high percent of rejections due to hemolysis may further be reduced by having all ED staff use these protocols, and by exploring other collection techniques in the literature that have been found to significantly decrease rejection rates.