This paper considers optimal admission and routing control in multi-class service systems in which customers can either receive quality regular service which is subject to congestion or can receive congestion-free but less desirable service at an alternative service station, which we call the self-service station. We formulate the problem within the Markov decision process framework and focus on characterizing the structure of dynamic optimal policies which maximize the expected long-run rewards. For this, value function and sample path arguments are used. The congestion sensitivity of customers is modeled with class-independent holding costs at the regular service station. The results show how the admission rewards of customer classes affect their priorities at the regular and self-service stations. We explore that the priority for regular service may not only depend on regular service admission rewards of classes but also on the difference between regular and self-service admission rewards. We show that optimal policies have monotonicity properties, regarding the optimal decisions of individual customer classes such that they divide the state space into three connected regions per class.

Introduction: Emergency department (ED) congestion is an ongoing threat to quality care. Traditional measures of ED efficiency use census and wait times over extended time intervals (e.g. per year, per day), failing to capture the hourly variations in ED flow. Borrowing from the traffic theory framework used to describe cars on a freeway, ED flow can instead be characterized by three fundamental parameters: flux (patients traversing a care segment per unit time), density (patients in a care segment per unit time), and duration (length of stay in a care segment). This method allows for the calculation of near-instantaneous ED flux and density. To illustrate, we examined the association between stretcher occupancy and time to physician initial assessment (PIA), seeking to identify thresholds where flux and PIA deteriorate. Methods: We used administrative data as reported to government agencies for 115,559 ED visits from April 1, 2014 to March 31, 2016 at a tertiary academic hospital. Time stamps collected at triage, PIA, and departure were verified by nosologists and used to define two care segments: awaiting assessment or receiving care. Using open-source software developed in-house, we calculated flow measures for each segment at 90-minute intervals. Graphical analysis was supplemented by regression analysis, examining PIA times of high (CTAS 1-3) or low (CTAS 4-5) acuity patients against ED occupancy (=density/staffed stretchers) adjusting for the day of the week, season and fiscal year. Results: At occupancy levels below 50%, PIA times remain stable and flux increases with density, reflecting free flow. Beyond 50% occupancy, PIA times increase linearly and flux plateaus, indicating congestion. While PIA times further deteriorate above 100% occupancy, flow is maintained, reflecting care delivery in non-traditional spaces (e.g. hallways). An inflection point where flux decreased with increased crowding was not identified, despite lengthening queues. Conclusion: The operational performance of a modern ED can be captured and visualized using techniques borrowed from the analysis of vehicular traffic. Unlike cars on a jammed roadway, patients behave more like a compressible fluid and ED care continues despite high degrees of crowding. Nevertheless, congestion begins well below 100% occupancy, presumably reflecting the need for stretcher turnover and saturation in subsegmental work processes. This methodology shows promise to analyze and mitigate the many factors contributing to ED crowding.

In this article, we introduce a recreational amenity—a greenbelt park—into a simple urban economic model. For multiple possible park placements, we solve for the associated equilibrium urban structure, including the equilibrium rent gradient, city boundary, total number of park visits, the overall utility level, and total vehicle miles traveled. We examine how these change with alternative park placement sites. We then show how two modifications of the basic model—allowing congestion at the site to affect site quality, and introducing the possibility of a substitute site at the city's periphery—affect our conclusions about how greenbelt location influences urban structure.

We study congestion periods in a finite fluid buffer when the net input rate depends upon a recurrent Markov process; congestion occurs when the buffer content is equal to the buffer capacity. Similarly to O'Reilly and Palmowski (2013), we consider the duration of congestion periods as well as the associated volume of lost information. While these quantities are characterized by their Laplace transforms in that paper, we presently derive their distributions in a typical stationary busy period of the buffer. Our goal is to compute the exact expression of the loss probability in the system, which is usually approximated by the probability that the occupancy of the infinite buffer is greater than the buffer capacity under consideration. Moreover, by using general results of the theory of Markovian arrival processes, we show that the duration of congestion and the volume of lost information have phase-type distributions.

The aim of this work was to study how machine milking (MM) carried out in suitable conditions affects teat wall thickness and teat canal length and their return after milking to pre-milking conditions, in comparison with other milk extraction methods considered biological referents: lamb suckling (LS), milk removal by catheter (RC) and hand milking (HM). Three Latin square experiments were designed, using 11 ewes in the first experiment (LS), 13 in the second (RC) and 12 in the third (HM). Each of the Latin squares was divided into two periods: in the first, the left gland of each animal was machine milked and the corresponding treatment (LS, RC and HM) was applied to the right gland. Subsequently, in the second period the extraction methods were interchanged. During the experimental period, 4 sampling days were carried out (2 in each experimental period), where ultrasound scans were taken before (B) and immediately after milking (A) and at 1 (1 h), 2 (2 h), 3 (3 h), 4 (4 h), 6 (6 h), 8 (8 h) and 10 (10 h) hours after milking finished. Teat wall thickness (TWT), teat wall area (TWA), teat end area (TEWA) and teat canal length (TCL) were measured in all the ultrasound images. MM increased TWT after milking compared with RC. TWT, TWA, TEWA and TCL were lower (P<0·05) in HM than in MM. No significant differences (P>0·05) were found between LS and MM for any variable. The extraction method affected the recovery time of the variables, with total teat recovery at 6 h after RC and 4 h after HM. In the case of LS, the TEWA and TCL values were recovered sooner, as of 3 h. Teat recovery time after MM was similar to the extraction method with which it was compared in each experiment. Thus, considering the similar increase in wall thickness and their recovery time compared with the reference methods, it was concluded that machine milking, carried out in optimum conditions and respecting the time interval between milkings usually applied on sheep farms (8–12 h), would not affect teat integrity. Moreover, given the variability observed in teat thickness recovery time between the different experiments, further research should be carried out to study which factors intrinsic and extrinsic to the animal may affect the teat wall thickness and recovery time after machine milking.

The aim of this work was to study the effect on teat wall thickness and canal length in sheep and goats of overmilking for 2 min (OM+2) and of milking with used (AL; +3000 milkings) and twisted (TL; 45°) liners in sheep and goats, as well as the effect of milking goats with liners designed for sheep (SL, shorter length and diameter than liners for goats). To this end, we performed four experiments in goats and three in sheep, in a Latin square design with two experimental periods. During the experimental period 4 controls were carried out, performing ultrasound scans before and immediately after milking to determine the teat wall thickness (TWT), teat wall area (TWA), teat end area (TEWA) and teat canal length (TCL). OM+2 caused a significant increase in TWT, TWA, TEWA and TCL in goats and in TWA, TEWA and TCL in sheep. Liner features had a strong influence on the variables studied; aged liners caused significant changes in TWT and TCL in goats and in TWT in sheep; twisted liners produced a significant effect on the increase of TWT and TCL in goats, without reaching significance level in sheep; and milking goats with sheep liners led to a significant increase in TWT, TWA, TEWA and TCL. In practice, it is therefore important to avoid overmilking and the use of worn-out liners. It is also necessary to use liners designed for the morphological features of each species, taking special care to carry out periodic liner positioning revisions to ensure the benefits of pulsation on the teat end. Finally, it would be necessary to carry out long-term experiments to study whether the increase in thickness observed in some experiments is sufficient to affect milking efficiency and mammary gland health status.

The merging of n independent traffic streams is studied. The arrival processes comprise random sized bunches of cars, the bunches being separated in time by random sized gaps. Within each bunch, cars are spaced at one time unit apart. Under a distributional assumption on the inter-bunch gaps exact formulae are found for (a) the mean delay to cars, (b) the first two moments of the post-merge bunch size, and (c) the distribution of the inter-bunch gaps in the post-merge process. It is shown that the distributional assumption is realistic and moreover that the distribution of (c) is of the same form. The arrival bunches have general size distribution with finite mean and variance.

A bound on the rate of convergence and sufficient conditions for the convergence of moments are obtained for the sequence of waiting times in the GI/G/1 queue when the traffic intensity is at the critical value ρ = 1.