The stationary distribution of the waiting time in a queueing system with negative customers and a bunker for superseded customers in the case of the LAST-LIFO-LIFO discipline

A queueing system with one service device and Poisson flows of ordinary and negative customers is considered. There is an infinite buffer for ordinary customers. A negative customer arriving at the system knocks out an ordinary customer queueing in the buffer and moves it to an infinite bunker and itself leaves the system. The customers from the bunker are served with a relative priority. The service durations for customers from the buffer and bunker have exponential distributions with different parameters. It is assumed that a negative customer knocks out the last customer queueing in the buffer and that the last customer queueing in the buffer or bunker is chosen to be served. for the system considered, the stationary waiting time distribution of ordinary customer arriving at the system is found in terms of the Laplace-Stieltjes transformation.     

The generalizedD [X] /D/1 queue: A flexible computer communications model

A generalization of theD ^[X] /D/1 queue is investigated, where independent and identically distributed (i.i.d) batches of customers arrive at a single-server queue periodically. The service requirement of a customer is a fixed constant equal for all the customers. In the time between two successive arrivals, the server can accommodate exactlyK1 customers. The queue size and the waiting time distributions for the infinite buffer queue are derived. Important numerical aspects are addressed and simple approximations for light and heavy traffic for various values ofK and Poisson distributed batches are proposed. Finally, the analysis for the finite queue is highlighted and its blocking probability derived.     

Optimal synthesis problems for Markovian queueing systems with several given characteristics

For an M/M/1/r queueing system and an M/M/1 system with threshold switching of service modes at the instant of the change in the number of customers as well as for the same system with threshold blocking of the flow of customers, the monotonic dependence of stationary characteristics (the mean number of serviced customers per unit time, the mean service cost per unit time, the probability of system downtime, and the mean waiting time of a customer in the queue) on the system parameters (the buffer size, the system usage, and the threshold of switching between the service modes) is used to solve the optimal synthesis problems for systems with several given stationary characteristics. The solution of a particular optimal synthesis problem is the optimum value of one of the above parameters.     

A multiserver queueing system with a finite buffer,blocking of a semi-Markovian input flow of customers,and removal of all customers from the system

A multiserver queueing system with a finite buffer, phase-type service at each server, and a semi-Markovian input flow of customers is considered. Arrival of customers at the system can be blocked during certain time intervals. The first customer arriving at the system after the arrival is unblocked removes all the customers from the system. A method is developed for calculating the stationary distribution of the number of customers in the system, and mathematical relationships for the mean time of a customer’s residence in the system are obtained.     

A service system for BT‘s major customers

Customer service excellence is regarded as one of the key differentiators of BTs product and service protfolio. This paper discusses, from a technical perspective, the major customer service system (MCSS), and how it is helping to achieve excellent customer service for BTs global and major customers.     

Queues with two units connected in series with a multiserver general bulk service in unit II

This paper analyses a queueing model consisting of two units I and II connected in series, separated by a finite buffer of size N. Unit I has only one exponential server capable of serving customers one at a time. Unit II consists of c parallel exponential servers and they serve customers in groups according to the general bulk service rule. The steady state probability vector of the number of customers waiting and receiving service in unit I and waiting in the buffer is obtained using the modified matrix-geometric method. Numerical results are also presented.     

Stationary characteristics of an M 2 X /M/n queue with hysteretic control of the input flow intensity

A multichannel queueing system with an unlimited queue length is considered. In the system, the service time and time intervals between arrivals of customer batches are characterized by exponential distributions and a hysteretic mechanism is applied to control the input flow intensity. The system receives two independent types of flows of customers one of which is blocked in the overload mode. An algorithm for determination of the stationary distribution of the number of customers and the stationary characteristics (the mean queue length, the mean time of waiting in the queue, the probability of a loss of customers) is proposed. The obtained results are verified with the help of a simulation model developed with the help of the GPSS World tools.     

A renewable single-server queueing system with priorities

A single-server queue with a triple priority system is considered in this paper. The server can fail during its occupation time and is sent for repair immediately.The stationary probabilities of the different states of the system are studied, under the assumption that the arrival time and the service time for the three kinds of customers, and the repair time, all have Poisson distributions with different parameters. The results obtained before, in [Mokaddis et al., Eighth International Congress for Statistics, Computer Science, Social and Demographic Research, Vol. 4, pp. 31–58 (1983)] in the case of a double priority, are derived from the present results as special cases. Moreover the mathematical expectation of the number of customers and the average waiting time of both kinds of customers and more characteristics of the system, in the case of double priority, are obtained. Also, in this paper, we study the system without priority, in the cases of both a triple priority system and a double priority system.     

带优先权与不耐烦顾客排队模型的模拟仿真

考虑一个有两类顾客到达的单服务台的排队系统。两类顾客的到达过程均为泊松过程,第一类顾客较第二类顾客具有强占优先权,且第二类顾客由于第一类顾客的到达而变得不耐烦,其＂耐性时间＂服从负指数分布。两类顾客的服务时间服从相同参数的负指数分布,服务规则是强占优先服务,在高负荷条件下用Matlab编程对此排队系统进行模拟仿真,为处理此类排队问题提供了一个新方法。     

A queueing system with stepwise randomly available additional space

In this paper we consider the steady state behaviour of a queueing system. The arrivals follow Poisson distribution and the service time distribution is exponential. Whenever the system size reaches a certain length, the system adds an additional space of unit size on every arrival with some probability and drops the additional space at the departure. Steady state probabilities are calculated explicitly and the average number of customers in the system is also obtained. Associating the cost with the rent of the additional space and the profit with each customer served, a criterion to obtain the optimum size of the ordinary space and the optimum number of unit size additional spaces to be hired is discussed.     

A multiserver queueing system with a interruptable semi-Markovian input flow of customers and customer removal from an infinite buffer

A queueing system with a interruptable semi-Markovian input flow of customers and customer removal from a buffer is considered. New customers arrive at servers or at the buffer only during time intervals when the access to the system is open. Customers are lost when the access to the system is closed at the instants of their arrivals. The intervals when the access to the system is open and closed alternate and their lengths are exponentially distributed. The first customer arriving at the system at an open-access interval removes all the customers from the buffer. Stationary characteristics of the system are found for the case when the buffer has an infinite capacity.     

A hybrid analysis/simulation for ATM performance with application to quality-of-service of CBR traffic

A discrete time queueing model for the performance of an ATM system is analyzed using matrix analytic methods. Time is segmented into slots with each slot equal to the transmission time of one ATM cell. The ATM system is modeled as a single server queue with Markovian arrivals and service time equal to one slot. The arrival process includes as a special case the superposition of on-off sources, possibly heterogeneous. The queueing model is of the M/G/1 type. By exploiting the structure of the M/G/1 type Markov chain, the complexity of the solution to the problem is reduced to only the inversion of a 2×2 matrix irrespective of the size of the Markov chain. This simplification allows us to investigate Constant Bit Rate (CBR) traffic performance (or quality-of-service) issues through a hybrid analysis/simulation approach. Specifically, we analyze the impact of on-off background traffic on the probability of consecutive cell losses, cell delay variation, and traffic shaper or playback buffer underflow and overflow probabilities of CBR traffic sources.     

排队取号服务系统的VHDL程序实现

排队取号服务系统广泛应用于银行、车站、电信等柜台营业部门,采用后能给顾客和工作人员带来极大便利。介绍一种基于VHDL语言实现自动排队取号的方法,并采用可编程逻辑器件加以实现和验证该排队取号系统不仅能实时动态显示当前取号顾客的编号和此前等待顾客的人数,还能显示当前空闲的柜台号以及准备接受服务的顾客编号。整个设计实用、简便,可靠性高,成本低廉,具有一定的实用推广价值。     

Stationary characteristics of MX/M/1 systems with two-speed service

An M^X/M/1 queueing system with threshold switching of service regimes at the instant of a change in the number of customers and the same system with threshold blocking of the flow of customers are considered. For these systems, an algorithm is proposed for determination of the stationary distribution of the number of customers and stationary characteristics (the mean queue length, the mean time of waiting in a queue, the variance of the queue length, the probability of the customer service for a system with blocking). For the case when the minimal number of incoming customers in a group is comparable with threshold value h, the stationary characteristics are found in an explicit form. For the system with threshold switching of service regimes (without blocking), two problems of optimal synthesis are solved. In these problems, the optimal values of threshold h and of the service intensity in the post-threshold regime are determined. The obtained results are verified with the help of simulation models developed with the help of the GPSS World software.     

Bandwidth Allocation Strategies in Wide-Band Integrated Networks

A common digital transmission facility in a wide-band integrated service digital network (ISDN) provides shared access to a community of heterogeneous users. Traffic demands from these users vary in their arrival rate, their service time, and their bit rate. In order for this type of communication system to handle its traffic demands with high efficiency and flexibility, a close control of access to the shared bandwidth is required. We model the system by a general multiserver queueing system where customers demand service from a random number of servers. If no waiting is allowed, this queueing model is readily analyzed, and various server allocation strategies can be studied. If the various access requests are queued for service, then the system calls for efficient strategies for allocating servers to waiting customers. In this case, exact analysis of the underlying queueing model becomes quite difficult. For this case, we present some analytic and simulation results of the performance of the system under several server allocation policies.     

Broadcast Disks with Polynomial Cost Functions

In broadcast disks systems, information is broadcasted in a shared medium. When a client needs an item from the disk, it waits until that item is broadcasted. Broadcast disks systems are particularly attractive in settings where the potential customers have a highly-asymmetric communication capabilities, i.e., receiving is significantly cheaper than transmitting. This is the case with satellite networks, mobile hosts in wireless networks, and Teletext system.The fundamental algorithmic problem for such systems is to determine the broadcast schedule based on the demand probability of items, and the cost incurred to the system by clients waiting. The goal is to minimize the mean access cost of a random client. Typically, it was assumed that the access cost is proportional to the waiting time. In this paper, we ask what are the best broadcast schedules for access costs which are arbitrary polynomials in the waiting time. These may serve as reasonable representations of reality in many cases, where the patience of a client is not necessarily proportional to its waiting time.We present an asymptotically optimal algorithm for a fractional model, where the bandwidth may be divided to allow for fractional concurrent broadcasting. This algorithm, besides being justified in its own right, also serves as a lower bound against which we test known discrete algorithms. We show that the Greedy algorithm has the best performance in most cases. Then we show that the performance of other algorithms deteriorate exponentially with the degree of the cost polynomial and approaches the fractional solution for sub-linear cost. Finally, we study the quality of approximating the greedy schedule by a finite schedule.     

Blocking probabilities in a loss system with arrivals ingeometrically distributed batches and heterogeneous service requirements

The authors analyze a generalization of the classical Erlang loss model. Customers of several types contend for access to a service facility consisting of a finite number of servers. Each customer requires a fixed number of servers simultaneously during an exponentially distributed service time, and is blocked on arrival if this requirement cannot be met. Customers of each type arrive in geometrically distributed batches, while the arrival of batches of each type is governed by a Poisson process. All relevant parameters may be type-dependent. The authors obtain the steady-state distribution of the number of customers of each type in the system (which turns out to have product form) and the blocking probabilities experienced by each customer type. In addition, the authors bring to light the connection between the model at hand and a method is proposed by L.E.N. Delbrouck (1983) for estimating blocking probabilities in an incompletely specified setting     

A method for calculating stationary queue distribution in a queuing system with flows of ordinary and negative claims and a bunker for superseded claims

A queuing system with one service unit and Poisson flows of positive and negative claims is considered. There is an infinite buffer for positive claims. A negative claim arriving at the system knocks out a positive claim waiting in the buffer and moves it to another infinite buffer (bunker). The claims from bunker are served with relative priority. If upon arrival of negative claim the buffer is empty, it leaves the system without affecting it. The service times for claims from buffer and bunker have exponential distributions with different parameters. A new method that provides efficient calculation of stationary distribution of the number of customers in buffer and bunker is proposed.     

Stationary characteristics of MX/M/1 systems with hysteretic switching of the service intensity

An M^X/M/1 queueing system with two-threshold hysteretic switching of the service intensity at the instants when the number of customers exceeds h ₂ and, then, decreases to the value h ₁ < h ₂ and the same system with the threshold locking of a flow of customers are considered. An algorithm is proposed for determination of the stationary distribution of the number of customers and stationary characteristics (the mean queue length, the mean time of waiting in a queue, the variance of the queue length, and the probability of the service of a customer for the system with blocking). Restrictions are imposed on the distribution of the number of incoming customers in a group to facilitate the determination of the stationary characteristics in an explicit form. The results are verified with the help of simulation models developed with the use of the GPSS World tools.     

Buffer Behavior for Mixed Input Traffic and Single Constant Output Rate

A queueing model with limited waiting room (buffer), mixed input traffic (Poisson and compound Poisson arrivals), and constant service rate is studied. Using average burst length, traffic intensity, and input-traffic mixture rate as parameters, we obtain relationships among buffer size, overflow probabilities, and expected message-queueing delay due to buffering. These relationships are portrayed on graphs that can be used as a guide in buffer design. Although this study arose in the design of statistical multiplexors, the queueing model developed is quite general and may be useful for other industrial applications.