Multitype branching process with non-homogeneous Poisson and contagious Poisson immigration

In a multitype branching process, it is assumed that immigrants arrive according to a non-homogeneous Poisson or a contagious Poisson process (both processes are formulated as a non-homogeneous birth process with an appropriate choice of transition intensities). We show that the normalized numbers of objects of the various types alive at time t for supercritical, critical, and subcritical cases jointly converge in distribution under those two different arrival processes. Furthermore, we provide some transient expectation results when there are only two types of particles.

Performance Evaluation of Stochastic Systems with Dedicated Delivery Bays and General On-Street Parking

As freight deliveries in cities increase due to retail fragmentation and e-commerce, parking is becoming a more and more relevant part of transportation. In fact, many freight vehicles in cities spend more time parked than they are moving. Moreover, part of the public parking space is shared with passenger vehicles, especially cars. Both arrival processes and parking and delivery processes are stochastic in nature. In order to develop a framework for analysis, we propose a queueing model for an urban parking system consisting of delivery bays and general on-street parking spaces. Freight vehicles may park both in the dedicated bays and in general on-street parking, whereas passenger vehicles only make use of general on-street parking. Our model allows us to create parsimonious insights into the behavior of a delivery bay parking stretch as part of a limited length of curbside. We are able to find explicit expressions for the relevant performance measures, and formally prove a number of monotonicity results. We further conduct a series of numerical experiments to show more intricate properties that cannot be shown analytically. The model helps us shed light onto the effects of allocating scarce urban curb space to dedicated unloading bays at the expense of general on-street parking. In particular, we show that allocating more space to dedicated delivery bays can also make passenger cars better off.

Impact of weather conditions on airport arrival delay and throughput

Purpose Weather events have a significant impact on airport arrival performance and may cause delays in operations and/or constraints in airport capacity. In Europe, almost half of all regulated airport traffic delay is due to adverse weather conditions. Moreover, the closer airports operate to their maximum capacity, the more severe is the impact of a capacity loss due to external events such as weather. Various weather uncertainties occurring during airport operations can significantly delay some arrival processes and cause network-wide effects on the overall air traffic management (ATM) system. Quantifying the impact of weather is, therefore, a key feature to improve the decision-making process that enhances airport performance. It would allow airport operators to identify the relevant weather information needed, and help them decide on the appropriate actions to mitigate the consequences of adverse weather events. Therefore, this research aims to understand and quantify the impact of weather conditions on airport arrival processes, so it can be properly predicted and managed. Design/methodology/approach This study presents a methodology to evaluate the impact of adverse weather events on airport arrival performance (delay and throughput) and to define operational thresholds for significant weather conditions. This study uses a Bayesian Network approach to relate weather data from meteorological reports and airport arrival performance data with scheduled and actual movements, as well as arrival delays. This allows us to understand the relationships between weather phenomena and their impacts on arrival delay and throughput. The proposed model also provides us with the values of the explanatory variables (weather events) that lead to certain operational thresholds in the target variables (arrival delay and throughput). This study then presents a quantification of the airport performance with regard to an aggregated weather-performance metric. Specific weather phenomena are categorized through a synthetic index, which aims to quantify weather conditions at a given airport, based on aviation routine meteorological reports. This helps us to manage uncertainty at airport arrival operations by relating index levels with airport performance results. Findings The results are computed from a data set of over 750,000 flights on a major European hub and from local weather data during the period 2015–2018. This study combines delay and capacity metrics at different airport operational stages for the arrival process (final approach, taxi-in and in-block). Therefore, the spatial boundary of this study is not only the airport but also its surrounding airspace, to take both the arrival sequencing and metering area and potential holding patterns into consideration. Originality/value This study introduces a new approach for modeling causal relationships between airport arrival performance indicators and meteorological events, which can be used to quantify the impact of weather in airport arrival conditions, predict the evolution of airport operational scenarios and support airport decision-making processes.

On Renting Edge Resources for Service Hosting

The rapid proliferation of shared edge computing platforms has enabled application service providers to deploy a wide variety of services with stringent latency and high bandwidth requirements. A key advantage of these platforms is that they provide pay-as-you-go flexibility by charging clients in proportion to their resource usage through short-term contracts. This affords the client significant cost-saving opportunities by dynamically deciding when to host its service on the platform, depending on the changing intensity of requests. A natural policy for our setting is the Time-To-Live (TTL) policy. We show that TTL performs poorly both in the adversarial arrival setting, i.e., in terms of the competitive ratio, and for i.i.d. stochastic arrivals with low arrival rates, irrespective of the value of the TTL timer. We propose an online policy called RetroRenting (RR) and characterize its performance in terms of the competitive ratio. Our results show that RR overcomes the limitations of TTL. In addition, we provide performance guarantees for RR for i.i.d. stochastic arrival processes coupled with negatively associated rent cost sequences and prove that it compares well with the optimal online policy. Further, we conduct simulations using both synthetic and real-world traces to compare the performance of RR with the optimal offline and online policies. The simulations show that the performance of RR is near optimal for all settings considered. Our results illustrate the universality of RR.

Technical Note—Approximating Systems Fed by Poisson Processes with Rapidly Changing Arrival Rates

In many operations management settings, the arrival process to the system exhibits clear nonstationarities. These nonstationarities may arise as a consequence of time-of-day effects, day-of-week effects, seasonalities, or stochastic fluctuations in the arrival rate. Tools that are developed for performance prediction and decision making when systems are stationary may not be valid in the nonstationary environment. This paper provides a generic, closed-form, and simple approximation tool for when the nonstationarities are caused by rapid fluctuations in the arrival processes.

Queues with path-dependent arrival processes

We study the transient and limiting behavior of a queue with a Pólya arrival process. The Pólya process is interesting because it exhibits path-dependent behavior, e.g. it satisfies a non-ergodic law of large numbers: the average number of arrivals over time [0, t] converges almost surely to a nondegenerate limit as $t \rightarrow \infty$. We establish a heavy-traffic diffusion limit for the $\sum_{i=1}^{n} P_i/GI/1$ queue, with arrivals occurring exogenously according to the superposition of n independent and identically distributed Pólya point processes. That limit yields a tractable approximation for the transient queue-length distribution, because the limiting net input process is a Gaussian Markov process with stationary increments. We also provide insight into the long-run performance of queues with path-dependent arrival processes. We show how Little’s law can be stated in this context, and we provide conditions under which there is stability for a queue with a Pólya arrival process.

Diffusion Approximation for Fair Resource Control—Interchange of Limits Under a Moment Condition

In a prior study [Ye HQ, Yao DD (2016) Diffusion limit of fair resource control–Stationary and interchange of limits. Math. Oper. Res. 41(4):1161–1207.] focusing on a class of stochastic processing network with fair resource control, we justified the diffusion approximation (in the context of the interchange of limits) provided that the pth moment of the workloads are bounded. To this end, we introduced the so-called bounded workload condition, which requires the workload process be bounded by a free process plus the initial workload. This condition is for a derived process, the workload, as opposed to primitives such as arrival processes and service requirements; as such, it could be difficult to verify. In this paper, we establish the interchange of limits under a moment condition of suitable order on the primitives directly: the required order is [Formula: see text] on the moments of the primitive processes so as to bound the pth moment of the workload. This moment condition is trivial to verify, and indeed automatically holds in networks where the primitives have moments of all orders, for instance, renewal arrivals with phase-type interarrival times and independent and identically distributed phase-type service times.

Optimizing a Multi-State Cold-Standby System with Multiple Vacations in the Repair and Loss of Units

A complex multi-state redundant system with preventive maintenance subject to multiple events is considered. The online unit can undergo several types of failure: both internal and those provoked by external shocks. Multiple degradation levels are assumed as both internal and external. Degradation levels are observed by random inspections and, if they are major, the unit goes to a repair facility where preventive maintenance is carried out. This repair facility is composed of a single repairperson governed by a multiple vacation policy. This policy is set up according to the operational number of units. Two types of task can be performed by the repairperson, corrective repair and preventive maintenance. The times embedded in the system are phase type distributed and the model is built by using Markovian Arrival Processes with marked arrivals. Multiple performance measures besides the transient and stationary distribution are worked out through matrix-analytic methods. This methodology enables us to express the main results and the global development in a matrix-algorithmic form. To optimize the model, costs and rewards are included. A numerical example shows the versatility of the model.