MAP 1, MAP2 /M/c retrial queue with guard channels and its application to cellular networks

In this paper, we investigate the impact of retrial phenomenon on loss probabilities and compare loss probabilities of several channel allocation schemes giving higher priority to hand-off calls in the cellular mobile wireless network. In general, two channel allocation schemes giving higher priority to hand-off calls are known; one is the scheme with the guard channels for hand-off calls and the other is the scheme with the priority queue for hand-off calls. For mathematical unified model for both schemes, we consider theMAP ₁,MAP ₂ /M/c/b, ∞ retrial queue with infinite retrial group, geometric loss, guard channels and finite priority queue for hand-off class. We approximate the joint distribution of two queue lengths by Neuts' method and also obtain waiting time distribution for hand-off calls. From these results, we obtain the loss probabilities, the mean waiting time and the mean queue lengths. We give numerical examples to show the impact of the repeated attempt and to compare loss probabilities of channel allocation schemes.     

Analysis of the queue-length distribution for the discrete-time batch-service Geo/G/1/K queue

In this paper, we consider a discrete-time finite-capacity queue with Bernoulli arrivals and batch services. In this queue, the single server has a variable service capacity and serves the customers only when the number of customers in system is at least a certain threshold value. For this queue, we first obtain the queue-length distribution just after a service completion, using the embedded Markov chain technique. Then we establish a relationship between the queue-length distribution just after a service completion and that at a random epoch, using elementary ‘rate-in = rate-out’ arguments. Based on this relationship, we obtain the queue-length distribution at a random (as well as at an arrival) epoch, from which important performance measures of practical interest, such as the mean queue length, the mean waiting time, and the loss probability, are also obtained. Sample numerical examples are presented at the end.     

不同价格水平下排队策略研究

在M/M/1排队中引入了不同的服务价格,基于"收益-成本"结构,以顾客和企业均追求利益最大化为出发点,在两种不可见情形下,研究了顾客均衡策略行为和企业最优服务定价决策,通过数值模拟,描述了休假期服务价格对顾客均衡策略的影响,以及几乎不可见情况下休假期服务价格对企业收益的作用和完全不可见情况下休假期服务价格随潜在到达率的变化情况,以及当企业获得最大收益时,正常工作期和休假期服务价格的关系.     

A unified algorithm for computing the stationary queue length distributions inM(k)/G/1/N and GI/M(k)/1/N queues

An iterative algorithm is developed for computing numerically the stationary queue length distributions in M/G/1/N queues with arbitrary state-dependent arrivals, or simply M(k)/G/1/N queues. The only input requirement is the Laplace-Stieltjes transform of the service time distribution.In addition, the algorithm can also be used to obtain the stationary queue length distributions in GI/M/1/N queues with state-dependent services, orGI/M(k)/1/N, after establishing a relationship between the stationary queue length distributions inGI/M(k)/1/N and M(k)/G/1/N+1 queues.Finally, we elaborate on some of the well studied special cases, such asM/G/1/N queues,M/G/1/N queues with distinct arrival rates (which includes the machine interference problems), andGI/M/C/N queues. The discussions lead to a simplified algorithm for each of the three cases.     

GI／PH／1休假排队系统队长的随机分解

对空竭服务、多重休假规则的GI/PH/1排队系统的稳态行为给出了详尽分析。在休假时间服从负指数分布情况下,讨论了到达点嵌入Markov链的结构、平衡条件和稳态队长。证明稳态队长可分解成两个独立随机变量之和。     

Queueing systems with inventory management with random lead times and with backordering

We investigate M/M/1/∞-systems with inventory management, continuous review, exponentially distributed lead times and backordering. We compute performance measures and derive optimality conditions under different order policies. For performance measures, which are not explicitly at hand, we present an approximation scheme for all possible parameter combinations. Although we cannot completely determine analytically the steady state probabilities for the system we are able to derive functional relations between interesting probabilities and show surprising insensitivity properties of several performance measures. For the approximations we develop an algorithm adapted to the system structure which suggests easy adaption to other systems.Work supported by Deutscher Akademischer Austauschdienst and KBN, Poland, Project D/02/32206.     

Bilevel control of degraded machining system with warm standbys, setup and vacation

In this paper, we study (N, L) switch-over policy for machine repair model with warm standbys and two repairmen. The repairman (R₁) turns on for repair only when N-failed units are accumulated and starts repair after a set up time which is assumed to be exponentially distributed. As soon as the system becomes empty, the repairman (R₁) leaves for a vacation and returns back when he finds the number of failed units in the system greater than or equal to a threshold value N. Second repairman (R₂) turns on when there are L(>N) failed units in the system and goes for a vacation if there are less than L failed units. The life time and repair time of failed units are assumed to be exponentially distributed. The steady state queue size distribution is obtained by using recursive method. Expressions for the average number of failed units in the queue and the average waiting time are established.     

Traffic flow through multi-lane tollbooths on a toll highway

We study the traffic states and queuing occurring in traffic flow on a toll highway with multi-lane tollgates. The traffic states change with increasing density and varying number of tollgates. When the manual-collection vehicles sort themselves into the tollgates, the queues occur just in front of the tollgates if the vehicular density is higher than a critical value. The queuing in front of tollgates is induced by the competition between the lane expansion and slowdown effects. When the lane expansion effect is superior to the slowdown effect, no queuing occurs. We derive the fundamental diagrams (current-density diagrams) for the traffic flow on the toll highway. The current saturates at the nearest tollgate at a low density and the saturation extends to the next-nearest tollgate with increasing density.     

<Emphasis Type="Italic">GI</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/1/∞ batch arrival queueing system with a single exponential vacation

In the article the queueing system of GI/G/1 type with batch arrival of customers and a single exponentially distributed vacation period at the end of every busy period is considered. Basic characteristics of transient state of the system are investigated: the first busy period, the first vacation period and the number of customers served during the first busy period. New results for the Laplace transform of the joint distribution of these three variables are obtained in dependence on the initial conditions of the system. This material is based upon work supported by the Polish Ministry of Scientific Research and Information Technology under Grant No. 3 T11C 014 26.     

A queueing model for customer rescheduling and no-shows in service systems

We study an M/M/1/K queue where customers can reschedule their appointments. Rescheduled customers show up with higher probabilities, incurring lower no-show costs, but rescheduling also frees up slots that may not be filled later, leading to wasted service capacity and lower throughput. The system manager aims to minimize the long-run average cost by controlling rescheduling policies. We derive conditions under which rescheduling should be allowed for different scenarios depending on whether customers can reschedule only once or multiple times.