ANALYSIS OF A CONTINUOUS TIME SM[K]/PH[K]/1/FCFS QUEUE:AGE PROCESS,SOJOURN TIMES,AND QUEUE LENGTHS

This paper studies a continuous time queueing system with multiple types of customers and a first-come-first-served service discipline. Customers arrive according to a semi-Markov arrival process and the service times of individual types of customers have PH-distributios. A GI/M/1 type Markov process for a generalized age process of batches of customers is constructed. The stationary distribution of the GI/M/1 type Markov process is found explicitly and, consequently, the distributions of the age of the batch in service, the total workload in the system, waiting times, and sojourn times of different batches and different types of customers are obtained. The paper gives the matrix representations of the PH-distributions of waiting times and sojourn times. Some results are obtained for the distributions of queue lengths at departure epochs and at an arbitrary time. These results can be used to analyze not only the queue length, but also the composition of the queue. Computational methods are developed for calculating steady state distributions related to the queue lengths, sojourn times, and waiting times.

Effects of pooling,specialization,and discretionary task completion on queueing performance

Pooling,unpooling/specialization,and discretionary task completion are typical operational strategies in queueing systems that arise in healthcare,call centers,and online sales.These strategies may have advantages and disadvantages in different operational environments.This paper uses the M/M/1 and M/M/2 queues to study the impact of pooling,specialization,and discretionary task completion on the average queue length.Closed-form solutions for the average M/M/2 queue length are derived.Computational examples illustrate how the average queue length changes with the strength of pooling,specialization,and discretionary task completion.Finally,several conjectures are made in the paper.

THE TRANSIENT SOLUTION FOR M/G/1 QUEUEWITH SERVER VACATIONS

In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are directly obtained from the transient solution. As will be seen this paper provides a intuitive and elegant method for studying transient solutions for M/G/1 queues with single server.

THE QUEUE-LENGTH DISTRIBUTION FOR M^x/G/1 QUEUE WITH SINGLE SERVER VACATION

This paper studies the bulk-arrival M-x/G/1 queue with single server vacation. By introducing the server busy period and using the Laplace transform, the recursion expression of the Laplace transform of the transient queue-length distribution is derived. Furthermore, the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are obtained. Especially some results for the single-arrival M/G/1 queue with single server vacation and bulk-arrival M-x/G/1 queue but with no server vacation can be derived directly by the results obtained in this paper.

Travel time function for basic link considering signal control in network traffic model

In order to describe the travel time of signalcontrolled roads, a travel time model for urban basic roads based on the cumulative curve is proposed. First, the traffic wave method is used to analyze the formation and dispersion of the vehicle queue. Cumulative curves for road entrances and exits are established. Based on the cumulative curves, the travel time of the one-lane road under stable flow input is derived. And then, the multi-lane road is decomposed into a series of single-lane links based on its topological characteristics. Hence, the travel time function for the basic road is obtained. The travel time is a function of road length, flow and control parameters. Numerical analyses show that the travel time depends on the supply-demand condition, and it has high sensitivity during peak hours.

Method of spillover identification in urban street networks using loop detector outputs

Quick and reliable identification of the traffic state is of critical importance to traffic control systems, especially when spillovers appear. Firstly, a calculation method for the occupancy per cycle under different traffic conditions were presented, based on the relationship between the three basic traffic flow parameters, speed, traffic flow and density. Secondly, the times at which the stopping and starting waves approach a loop detector were confirmed using the traffic wave models modified by a kinematic equation. Then, the threshold of occupancy, which characterizes the appearance of spillovers, was determined by the premise that the stopping and starting waves had the same speed. At last, the accuracy and usability of the new method were verified by VISSIM simulation, using the ratio of misjudgment as the evaluation index. The results show that the ratio of misjudgment of the new method is about 11.36% compared to 17.65% of the previous method.

Distributed Packet-Aware Routing Scheme Based on Dynamic Network Coding

In this paper, we study transmission of packets with time constraints in cooperative 5G wireless networks. As we know, the packets which are transmitted with large delay become useless and have to be dropped. In order to minimize packet dropping probability, we consider multiple transmission methods and integrate packet scheduling with adaptive network coding method selection. Firstly we introduce queue length to obtain the gain of network. Based on this, we present the dynamic coding-aware routing metric, which can increase potential coding opportunities. Moreover, we propose a distributed packet-aware transmission routing scheme based on the above routing metric, which can discover the available paths timely and efficiently. Simulation results show that the proposed method can reduce average packet dropping probability with lower computational complexity.

An efficient priority service model with two-level-polling scheme

This paper considers an efficient priority service model with two-level-polling scheme which the message packets conform to the discrete-time Geom/G/1 queue with multiple vacations and bulk arrival. By the embedded Markov chain theory and the probability generating function method, we set up the mathematics functions and give closed form expressions for obtaining the mean cyclic period （MCP）, the mean queue length （MQL） and the mean waiting time （MWT） characteristics, the analytical results are also verified through extensive computer simulations. The performance analysis reveals that this priority polling scheme can gives better efficiency as well as impartiality in terms of system characteristics, and it can be used for differentiating priority service to guarantee better QoS and system stability in design and improvement of MAC protocol.

Secure and Optimal LOADng Routing for IoT with Composite RoutingMetric

Security is the one of the major challenges for routing the data between the source and destination in an Internet of Things(IoT)network.To overcome this challenge,a secure Lightweight On-demand Ad hoc Distancevector—Next Generation(LOADng)Routing Protocol is proposed in this paper.As the LOADng protocol is the second version of Ad Hoc On-Demand Distance Vector(AODV)protocol,it retains most of the basic functionality and characteristics of AODV.During the route discovery process,the cyclic shift transposition algorithm(CSTA)is used to encrypt the control packets of the LOADng protocol to improve its security.CSTA approach only derives transposition and substitution without product cipher with respect to input data.Besides this,for choosing the best probable path between the source and destination,routing metrics such as link quality Indicator(LQI),hop count(HC)and queue length(QL)are included in the control packets.The data is then securely sent using CSTA using the optimal secure path selected.Experimental Results depict that the proposed secure and optimal LOADng(SO-LOADng)using CSTA encryption obtains better throughput,delivery ratio encryption time and decryption time than the existing state-ofart approaches.

The Queue Length Distribution for M/G/1 Queue with Delay Single Server Vacation

In this paper we study the transient and equilibrium distributions of the queue length for the M/G/1 queueing system with delay single server vacation.By the server busy period and the Laplace transformation we directly obtain the recursion formula of the L transformation of the transient queue length distribution at any time t , as well as the recursion formula of the equilibrium distribution for calculating conveniently.Furthermore we obtain the stochastic decompositions of the queue length and waiting time in equilibrium.

Queue Size Distribution of Geo/G/1 Queue Under the Min(N,D)-Policy

This paper considers a discrete-time Geo/G/1 queue under the Min（N, D）-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first （Min（N, D）-policy）. By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of tile transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n＋. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution, l^trthermore, the important relations between the steady state queue length distributions at different time epochs n , n and n＋ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.

An M/G/1 Queueing System with Delay Server Vacations

In this paper we study the transient property of the queue length for the M/G/1 queueing system with delay server vacations.Using the server busy period and the Laplace transformation we directly obtain the recursion formula of the L transformation of the transient queue length distribution at time t , and also the recursion formula of the equilibrium distribution for calculating conveniently.As will be seen, this paper provides an intuitive and elegant method for studying transient properties of M/G/1 type queueing systems.

Analysis of Stationary Queue Length Distribution for Geo/T-IPH/1 Queue

In this paper we study a Geo/T-IPH/1 queue model,where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states.The queue model can be described by a quasi-birth-anddeath(QBD)process with countably phases.Using the operator-geometric solution method,we first give the expression of the operator and the joint stationary distribution.Then we obtain the probability generating function(PGF)for stationary queue length distribution and sojourn time distribution,respectively.

Optimal Control Policy of M/G/1 Queueing System with Delayed Randomized Multiple Vacations Under the Modified Min(N,D)-Policy Control

Based on the number of customers and the server’s workload,this paper proposes a modified Min(N,D)-policy and discusses an M/G/1 queueing model with delayed randomized multiple vacations under such a policy.Applying the well-known stochastic decomposition property of the steady-state queue size,the probability generating function of the steady-state queue length distribution is obtained.Moreover,the explicit expressions of the expected queue length and the additional queue length distribution are derived by some algebraic manipulations.Finally,employing the renewal reward theorem,the explicit expression of the long-run expected cost per unit time is given.Furthermore,we analyze the optimal policy for economizing the expected cost and compare the optimal Min(N,D)-policy with the optimal N-policy and the optimal D-policy by using numerical examples.

ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS Ⅱ： M（n）/G/1/K

We study a single-server queueing system with state-dependent arrivals and general service distribution, or simply M（n）/G/1/K, where the server follows an N policy and takes multiple vacations when the system is empty. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirements are the Laplace-Stieltjes transforms of the service time distribution and the vacation time distribution, and the state-dependent arrival rate. The computational complexity of the algorithm is O（K^3）.

ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS I:G/M(n)/1/K

In this paper we study a queueing system with state-dependent services and state-dependent vacations, or simply G/M（n）/1/K. Since the service rate is state-dependent, this system includes G/M/c and G/M/c/K queues with various types of station vacations as special cases. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirement is the Laplace-Stieltjes transform of the interarrival distribution as well as the state-dependent service rate and state-dependent vacation rate. In a subsequent companion paper, we study its dual system M（n）/G/1/K queue with statedependent vacations.

Methods for determining unimpeded aircraft taxiing time and evaluating airport taxiing performance

The objective of this study is to improve the methods of determining unimpeded（nominal） taxiing time,which is the reference time used for estimating taxiing delay,a widely accepted performance indicator of airport surface movement.After reviewing existing methods used widely by different air navigation service providers（ANSP）,new methods relying on computer software and statistical tools,and econometrics regression models are proposed.Regression models are highly recommended because they require less detailed data and can serve the needs of general performance analysis of airport surface operations.The proposed econometrics model outperforms existing ones by introducing more explanatory variables,especially taking aircraft passing and over-passing into the considering of queue length calculation and including runway configuration,ground delay program,and weather factors.The length of the aircraft queue in the taxiway system and the interaction between queues are major contributors to long taxi-out times.The proposed method provides a consistent and more accurate method of calculating taxiing delay and it can be used for ATM-related performance analysis and international comparison.

Estimation of Incident-Induced Congestion on Signalized Arteries Using Traffic Sensor Data

This paper describes how to derive quantitative information about the effect of traffic incidents on urban traffic flow from the raw measurements detected by sectional loop sensors. 3-he two critical parame- ters of the travel delay and queue length, which reflect the temporal and spatial properties of inci- dent-induced congestion, cannot be directly determined from commonly used loop sensors. The modified queuing diagram is used here to quantify incident-induced queues and travel delays on signalized arteries using sensor data from the targeted and upstream links. The method is tested using data generated by the VISSIM simulation model, with results indicating its efficiency and accuracy with an average relative travel delay error of 18.67% for all samples which falls to 8.07% for high volume and very high volume conditions.

A case study on multi-lane roundabouts under congestion:Comparing software capacity and delay estimates with field data

Existing studies on modern roundabouts performance are mostly based on data fron： singe lane roundabouts that are not heavily congested. For planners and designers interested in building multilane roundabouts for intersections with potential growth i~ future traffic, there has been a lack of existing studies with field data that provide reference values in terms of capacity and delay measurements. With the intent of providing such reference values, a case study was conducted by using the East DowlinC Road Roundabouts in Anchorage, Alaska, which are currently operating with extensive queues during the evening peak hours. This research used multiple video camcorders t（ capture vehicle turning movements at the roundabouts as well as the progressior~ of vehicle queues at the roundabout entrance approaches. With these video records, the number of vehicles in the queues can be accurately counted in any single minute during the peak hours. This study shows that unbalanced entrance flow patterns （i.e., ~ne entrance has significant higher flow than others） can intensify the queue and delay fo., the overall roundabouts. Then various software packages including RODEL, SIDRA and VISSIM were used to estimate several performance measurements, such as capacity. queue length, and delay, compared with the collected field data. With the comparison, it is found that all the three software packages overestimate multi-lane roundabout ca pacity before calibration. With default parameters, SIDRA and VISSIM tend to underes timate delays and queue lengths for the multi-lane roundabouts under congestion, while RODEL results in higher delay and queue length estimations at most of the entrance approaches.