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Mobile Survey on Simulation for Networks

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Simulation and modeling of mobile protocols
                                    Mobile computing survey




              ...
TABLE OF CONTENTS


SIMULATION AND MODELING OF MOBILE PROTOCOLS ........................................................ 3...
Simulation and modeling of mobile protocols

Abstract
         Mobile computing protocols are becoming one of the most imp...
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Mobile Survey on Simulation for Networks

  1. 1. Simulation and modeling of mobile protocols Mobile computing survey Edwin Hernandez David Witter Mobile Computing – CIS 6930 Dr. Sumi Helal Feb 24th, 1999
  2. 2. TABLE OF CONTENTS SIMULATION AND MODELING OF MOBILE PROTOCOLS ........................................................ 3 ABSTRACT ............................................................................................................................................ 3 INTRODUCTION - NOMADIC COMPUTING OVER THE INTERNET................................................................. 3 Address binding................................................................................................................................ 4 Network Infrastructure...................................................................................................................... 4 TCP connection management............................................................................................................ 5 MOBILITY PERFORMANCE.............................................................................................................. 6 HAND-OFF MANAGEMENT ALGORITHMS FOR URBAN AND SUB-URBAN ENVIRONMENTS UNDER REALISTIC VEHICLE MOBILITY CONDITIONS ........................................................................................................... 6 PERFORMANCE OF TRANSPORT PROTOCOLS OVER A MULTICASTING-BASED ARCHITECTURE FOR INTERNET HOST MOBILITY .................................................................................................................................... 7 PERFORMANCE E VALUATION OF MOBILE IP PROTOCOLS IN A WIRELESS ENVIRONMENT ......................... 8 REPLICATED SERVERS FOR IP-HOST MOBILITY....................................................................................... 10 ANALITICAL SIMULATION OF MOBILE NETWORKS .............................................................. 13 MOBILITY AND PERFORMANCE MODELING IN CELLULAR COMMUNICATION NETWORKS .......................... 13 Network Modeling .......................................................................................................................... 13 Cell modeling ................................................................................................................................. 15 REFERENCES................................................................................................................................... 18 2
  3. 3. Simulation and modeling of mobile protocols Abstract Mobile computing protocols are becoming one of the most important issues in state-of-the-art technologies. In this paper we will provide important issues in terms of modeling and simulation of mobile protocols. First, the survey discusses the theoretical issues in mobile or nomadic computing environment, afterwards some performance measurements papers are explained, they show simulations done to routing and hand-off optimizations. Finally, an analytical point of view is presented using queuing theory analysis in pico-cell networks. Introduction - Nomadic computing over the internet There are several answers to the problem of mobility, mobile-IP is one of them, but there are other frameworks found for instance in [Li98], where an universal personal computing (UPC) paradigm is presented. The term nomadicity refers to the system support needed to provide a rich set of computing and communication capabilities and services for mobile users in a transparent, integrated and convenient form as they move between different places. The desired characteristics for nomadicity include independence of location, motion, computing platform, communication device, and communication bandwidth, and the widespread availability of access to remote files, systems and services. There are some other standards for nomadicity, such as the Universal Personal Telecommunication, studied by the CCITT (ITU), which is based on the intelligent network architecture and focused on extending point-to-point connection-oriented services provided by the public switched telephone network to mobile users. In addition to those efforts, the Telecommunications Information Networking Architecture (TINA) has defined and validated an open architecture for telecommunications systems providing personal mobility functions. Both frameworks, as explained before are designed to be applicable in the Intelligent Network (IN) and Broadband ISDN (Integrated Services Digital Network). The UPC paradigm presented by [Li98] follows these design issues: • Only regular users of the internet are considered, each user should belong to a home network, a place where the user is properly registered. • Each mobile user has a service profile at her home network where all the services are defined. • Services and terminal control have to be logically separated. • Each user and her current terminal has to be identified by the Logical User Identifier (LIU) and Logical Terminal Identifier (LTI), respectively, that are independent of each others as well as their curretn location. 3
  4. 4. • Location information management of mobile objects is a key issue on UPC, the algorithms for searching and updating locations of mobile users and terminals should not adversely burden the internet in terms of traffic overhead and protocol processing. • Adaptation capabilities should be provided to harmonize the differences in operating environments, input, output, display and storage formats. • Certain intelligent agents may be incorporated to optimize the UPC operations through optimal functional divisions between terminals and networks. Address binding To enable personal mobility, a logical user identifier or LUI is needed to uniquely and directly identify a user irrespective of a terminal used. The LUI is used as the basis for sending and receiving messages and for charging a user for services. The terminals are identified by the LTI regardless of whether they are fixed or mobile. LUI should be unique and it might be a number or a name or even a picture, it might be the user@domain string. The IP address could be the analog to the LTI. Network Infrastructure It is composed by a User’s Home Agent (UHA), a Terminal’s Home Agent (THA) and a Foreign Agent (FA) which are configured in each self-administrative domain of the conceptual multi-network internet architecture to support personal and terminal mobility in UPC. User’s Home Agent (UHA): Each mobile user has a home network. The UHA in each network maintains a list of users calling the network home, and the pertinent information for each user, including service profile and location information. Terminal’s Home Agent (THA): The network should have a THA which maintains a home list of database identifiers of all mobile terminals that call the network home. They are the mobile hosts in mobile-ip. Terminal related information such as LTI, terminal profile, terminal authentication key, and current terminal location are stored in the THA. Foreign Agent (FA): As mobile users and terminals migrate over the internet, they need to access network computing resources and services from different networks connected to the internet. Each network serving mobile terminals should have a FA which enables users and terminals to be temporarily associated with the network. Each FA should provide two list one of visiting users and another one of visiting terminals. There is a binding to the UHA and THA to enable packet redirection. 4
  5. 5. TCP connection management Another important issue is the TCP connection management. TCP utilizes the three way handshake protocol, with a sequence of ACK – SYN – ACK, we have to recall the state machine for the TCP handshake defined in the TCP protocol.. In [Li98] is proposed three different solutions for mobile communication in TCP links. a) a Transparent Solution b) The TCP layer solution c) the middleware layer solution. In the Transparent Solution, the UHA has two finite states machines, it establishes a communication link using TCP between the source and then initiates a communication link to the Mobile Terminal (MT) or host. In fact [Li98] point out that the TCP connection between the UHA and the MT is supported by mobile-ip. However, movements of the MT will require routing optimization and cache validation techniques. Meanwhile the TCP Layer Solution , the source request to set up a connection to the UAH using an IP address of the MT. The UHA transfers the message to the MT, the message is tunneled and the MT piggyback the source. The TCP layer of the source is modified with the new IP address piggybacked by the MT. The main problem with this solution is the lack of transparency between the source and the destination, and this modification should be taken into consideration by the IETF which is not feasible. Finally the Middleware Layer Solution, in which the middleware is aware of the mobility of the MT at the UHA, therefore when the MT is moved and the directory service is requested the middleware should provide the source of information with updated addresses. This is similar to the TCP layer solution but it can be implemented in alignment with OSI principles. 5
  6. 6. Mobility Performance A common subject for research in mobile computing is performance of protocols and wireless simulation. At the physical access level, one can discuss hand-off issues between micro and macrocells. Moving to a higher level, issues involving the performance of Mobile IP versus Route Optimization Mobile IP are of keen importance as to which will be implemented in the future Internet. Another solution to mobility in IP is multicasting. This approach is promising due to the mobile host not needing to change IP addresses as it roams. Finally, a paper on replicated home-agents improving the load balance and availability. Hand-off Management Algorithms for Urban and Sub-urban Environments Under Realistic Vehicle Mobility Conditions While studying mobile computing and the challenges this field faces, one begins to realize that many of the problems parallel those faced by the cellular communication community. This paper discusses ways to lower the number of hand-offs needed when traveling through an urban area. The technique discussed here for cellular service could be targeted at the same challenge facing mobile computing. Before begin, the basics must be discussed. In a wireless environment, there are two types of coverage. Microcells usually provide coverage to congested areas such as an airport or business area. These are also called hot spots. Microcells cover an area with a radius of approximately 100m. Macrocells, on the other hand, are much larger and usually cover and area with several microcells within it. Macrocells are responsible for providing service to the suburban area as well as travelers through the urban area. See the figure below. Macrocell Microcells The process used to determine whether a user should be handed from the macrocell to the microcell depends on the classification of the user. A fast user, one that is travelling quickly through the region, would be assigned to the macrocell. A slow user, one that may be seated at a conference, would be 6
  7. 7. assigned to a microcell. This scheme works well except when a user is travelling through the region but is slowed considerably by a congested area with many traffic lights and is classified as slow. Under the current approach, the user would experience many hand-offs from one macrocell to the other. This method is grossly inefficient and increases the chance of the user becoming disconnected. Dr. Iera of the University of Reggio Calabrai, Italy [Iera08] purposed a solution to this problem. A fast user connected to the macrocell is given a time bonus when he reaches the border of a microcell. If the user travels through the microcell in time less than t_threshold, the user gets keeps 100% of the time bonus for the next microcell. If the traveler takes time less than t_threshold + time bonus, but greater than t_threshold, the time bonus us decreased for the next microcell. If the traveler takes more time than t_threshold + time bonus, then the traveler is immediately assigned to a microcell. In order to test this method, an elaborate traffic simulator was used in conjunction with the newly purposed algorithm. Varying the number of traffic lights as well as varying the light duration set the simulator parameters. Results were rather promising, as the average number of hand-offs per call decreased from 4.25 to 2.8. This improvement came at a cost though, as the number of calls blocked and forcefully terminated increased slightly with the new algorithm. This drawback can be contributed to the overloading of the macrocell in this scheme. Since the drawback seems small compared to the improvement in the number of hand-offs, this algorithm show promise for both the wireless communication environment. Performance of Transport Protocols over a Multicasting-based Architecture for Internet Host Mobility Although Mobile IP is gaining momentum towards being the standard, other solutions to mobility have been researched. One of those possible solutions is to use IP multicasting. IP multicasting provides packet delivery to location independent addresses and allows hosts to leave and join multicast groups. These abilities parallel the needs of host mobility in the wireless network environment. Jayanth Mysore and Vaduvur Bharghavan wrote this paper to explore the performance of Mobility Support using Multicasting in IP (MSM-IP) versus the standard Mobile IP protocol. In order to provide more complete results, both UDP and TCP were run over both MSM-IP and Mobile IP. Before discussing the results, the reader needs to understand how MSM-IP and Mobile IP work. In Mobile IP, each mobile host has its own home address. When the host moves from its home subnetwork to another, the mobile host receives a care-of-address. The care-of-address is a dynamic identifier that reflects the current point of attachment. When a correspondent host sends packets to the mobile host, the packets first go to the home agent. The home agent, who knows the care-of-address, forwards these packets to the mobile host. The mobile host, on the other hand, can send packets directly to the correspondent host. Thus, the name triangle routing originated. MSM-IP takes advantage of multicast routing to support host mobility. Multicast routing uses the virtual interconnection of tunnels over the existing internet. The source of data packets is the root of the 7
  8. 8. distribution tree, while the mobile host would be at lowest level. When a mobile host moves to a different network, it sends an IGMP registration message to the local multicast router. Due to common case mobility, the new multicast router will be close to the previous multicast router that was servicing the mobile host. Therefore, on the lowest level of the distribution tree will have to be modified making handoff with MSM-IP efficient. In order to test UDP performance with MSM-IP, 16 different test were run. The variables for each test were cold versus hot switching, uploading or downloading, 100Kbps or 400Kbps throughput and constant versus Poisson traffic distributions. Cold switching means the mobile host handed of before registering with the new network, while hot switching means the mobile host did register with the new network before handoff. Performance results were impressive as the maximum packet loss was 1 and the maximum number of duplicates was 3. In most cases thought, the number of duplicates was 0. To study the performance of TCP, the authors compared the distribution of the sequence numbers of the packets received to time during a switch. A constant slope on a graph would represent a constant steam of data uninterrupted during a switch. MSM-IP performed well, only showing less than a two- second delay before full recovery. When compared to Mobile IP, MSM-IP once again faired well. MSM- IP showed a significant performance gain, especially when the network was simulated with a larger delay. With a delay larger than 100ms, ACKs sent by the mobile host from its new location are not recognized, so the correspondent host continues to send packets to the old interface. Since the mobile host is no longer at this interface, all the data packets get lost. These lost data packets are interpreted as network congestion, and TCP consequently slows down transmission. MSM-IP does not have this problem, as the mobile host does not need to change multicast addresses. This paper has presented a reasonable alternative to Mobile IP through MSM-IP. MSM-IP uses multicasting so that packets destined for a mobile host do not need to travel through a home agent. It also reduces the number of packets lost during handoff because the correspondent host does not need a binding update to learn the new care-of-address. Although MSM-IP looks like a promising alternative, it is not a realistic widely-used solution because an effective IP multicasting infrastructure covering the entire internet is not in place. Performance Evaluation of Mobile IP Protocols in a Wireless Environment As the need for mobile access to the internet increases, solutions for IP in a wireless environment are needed. The two protocols with the most momentum are Mobile IP (MIP) and Route Optimization Mobile IP (ROMIP). In this paper, the performance in terms of overhead for control, packet delay and packet loss for both MIP and ROMIP are compared using simulation. 8
  9. 9. In order to discuss the performance measurements of the two protocols, the differences between the protocols must be discussed. Traditional MIP uses triangle routing, as the packet path from the correspondent host to the mobile host is different than from the mobile host to the correspondent. This is because the correspondent host only knows the mobile host’s home address. Any packet sent to the Correspondent Mobile Host Host home address is tunneled by the home agent to the mobile host’s care-of-address. One can see from the diagram that there is a certain amount of inefficiency in this method. ROMIP tries to address this Home Agent inefficiency. With ROMIP, correspondent host sends packets directly to the mobile host. The correspondent host maintains a cache of care-of-addresses for mobile hosts receiving packets, which allows the correspondent to send packets directly to the mobile host. Whenever a mobile host moves to another foreign subnet, the mobile host must send a binding update to both its home agent and the previous foreign agent. The home agent then sends a binding update to any correspondent host that needs the new care-of- address. The previous foreign agent uses the binding update to forward any packets it receives to the differently located mobile host. This forwarding continues until all the correspondent hosts have updated their care-of-address for the mobile host. The results from the simulation are what one would expect. The ROMIP protocol outperformed the traditional MIP when the session size (time) was substantial (>100kbit). When the session time was smaller than this, the overhead needed for ROMIP outweighed the benefit from the route optimization. As the session size increased past 100kbits, ROMIP’s end-to-end packet delay remained constant while MIP’s skyrocketed exponentially. The greater performance observed for ROMIP at higher session lengths can be contributed to two factors. First, the route between the correspondent host and the mobile host must be physically shorter due to the definition of a triangle. If the physical distance is shorter, the transmission time will also be shorter. Included in this factor is that the home agent requires processing time to tunnel packets to the mobile host. These two delays contribute to a constant delay for every packet sent. A second factor contributing for the higher performance is the flooding of home agents. In MIP, every packet sent to a mobile host must pass through the home agent. If the home agent is servicing several hosts that roaming, packet congestion at the home agent becomes a serious problem. This explains why the end-to-end packet delay for MIP increased exponentially with longer session times. In this paper, two popular approaches to host mobility in a wireless environment were compared through simulation. The Route Optimization Mobile IP outperformed the standard Mobile IP at longer session lengths. At session lengths less than 100kbits, ROMIP performs poorly due to the overhead 9
  10. 10. required for route optimization. Any session exceeding 100Kbits allows the route optimization to be beneficial. Since most sessions are longer than 100kbits, ROMIP seems to be the most attractive solution. Replicated servers for ip-host mobility In [Jue98], an extension for the mobile-ip protocol is presented in terms of the use of replicated home-agents to handle multiple request for different mobile hosts groups. Replication will provide load- balancing and avoid the single-point of failure provided by the home-agent. We have to recall that in the mobile-ip architecture, a foreign agent and a home agent are required for mobility. The mobile host moves to another network where the foreign agent expect to receive a `registration packet in order to keep track of the mobile host and make the home-agent forward the information to the proper destination. The approach followed here consists in the use of not one, if not several replicated home-agents, using different techniques to access and load balance between each other. The basic mobile-ip protocol has evolved out of the efforts of the mobile IP working group and specifies mobility support under Ipv4. The home-agent is usually a router or host in the mobile host’s home network which maintain mobility bindings (a permanent IP address to a temporary IP address translation) for the mobile host. Meanwhile, the foreign agent may be a router or host in the network where the mobile host is visiting, and it provides the mobile host with a temporary IP address. If the number of available IP addresses in the foreign network is limited, then the foreign agent may act as a proxy server for the mobile host, in this case the temporary IP address will belong to the foreign agent’s IP address. The protocol proposed in [Jue98] the mobile host will have the IP addresses of all the home agents in the home network. When the mobile hosts sends a registration request (issue of Mobile-IP protocol). It will randomly choose one of the home agents to service the request. As defined in the mobile-IP protocol, it is assumed that each mobile registration request has an unique identification and a lifetime which defines the time for which the registration is valid. This time is defined by Treg. The registration packet also contains the IP address of the mobile host, and the temporary IP address of the mobile host. As part of the mobility binding, the agent maintains the following information: 1. The unique registration numbers 2. The permanent IP address of the mobile host 3. The temporary IP address of the mobile host 4. A boolean variable called PROXY (on or off), which indicates if the proxy is on or not. If proxy is ON, then the home agent is acting as a proxy for the mobile host and responds with a proxy ARP reply whenever an ARP query is received for the mobile host. If it is off, a different home agent is serving the mobile host. 10
  11. 11. 5. Treg which defines the time for which the registration is valid. With multiple home agents load balancing will be achieved by allowing a home agent to transfer control of a mobile host to another home agent based on some load balancing algorithm. The load balancing algorithms consist of two parts: a) A transfer policy which determines when a transfer should take place and b) a Selection policy which determines to which home agent the control should be transferred. In fact, [Jue98] choose different load balancing strategies, for instance for policy transfer, three approaches were made: • Timer-based: In this approach, each home agent maintains a timer for each mobile host that is serving. The time value will be referred to as the stream transfer time and will be denoted as Tstt. When a home agent acquires control of a mobile host, it starts the timer after the first packet for the mobile host is received. When Tstt expires, a new home agent is selected, and a registration request is forwarded to a new home agent. • Counter-based: This approach is different, the home agent counts the number of packets forwarded to each mobile host. When the counter reaches a specified limit, the home agent transfers the registration of the mobile host to another home-agent. This counter is referred as Tstc • Threshold-based: For each mobile host, the home-agent maintains a count of the number of packets in its queue which are destined to the mobile host. When the number of packets in the queue for a given mobile host exceeds the threshold, the home-agent forwards that mobile host’s registration to another home agent. The threshold value will be referred as Tsth There is not much difference between policies requires some extra overhead, in other words, re-register the mobile host to a new home-agent and selection procedure involved. As shown here is expected to see that the Timer-based approach will lead to switching from home-agents even though the traffic is zero. This situation is not present in the counter based approach. The values for thresholds and timeouts were modeled in the paper. There is another factor in this protocol, and it is the selection of the next home-agent, three different policies where also studied in this paper: • Random policy: The next home-agent is selected randomly from all home agents, including the home agent attempting the transfer. • Round-robin policy (RR): The home agent are logically ordered and the next home agent is selected using a simple round-robin policy 11
  12. 12. • Join the Shortest Queue (JSQ) policy. The home agent which has the minimum number of queued packets is selected as the next home-agent. Similar to the random policy, the current home-agent may also be selected as the next home-agent. Random and RR are easier to implement, intuitively JSW will provide a better performance, but leading to a lot of overhead. The simulation was executed using the following assumptions: • There are N identical home-agents • A home-agent is modeled as a single-server queue which servers both data packets and overhead packets • The arrival process is modeled as a MMPP (Markov Modulated Poisson Process) with arrival rate λ during an ON period and 0 during an off period. • The duration of an off period is exponentially distributed and with a mean 1/σ1 seconds • The duration of the on period is exponentially distributed and with a mean 1/σ2 seconds • The service time of a data packet is defined by µ per second • The service time of an overhead packet is exponentially distributed with a service rate of µ/C packets per second, by changing C it is possible to model different overhead costs. • The registration overhead is negligible The analytical model was tested using non-preemptive queues and shadow-servers approximations, having the sources or mobile hosts equally distributed and assigned to the home-agents and burst-level load balancing, where Tstt is set to an infinite value and is used as a reference point for comparison with the proposed load balancing scheme All the simulative analysis lead to conclude that by providing a mechanism which allows incoming packet streams to be transferred from one home-agent to another, the system’s performance is improved taken as a reference a single-server. The results provided here showed that a random policy yielded to modes load balancing gains, and the JSQ policy performs much better than the random selection. 12
  13. 13. ANALITICAL SIMULATION OF MOBILE NETWORKS Mobility and performance modeling in cellular communication networks A simply analytical model for cellular communication networks can be found in [Camar98], where the model assumes a finite population of mobiles moving in a finite number of cells. This model tries to evaluate the Fixed Channel Allocation (FCA) factor, as well as, user load, mobility and distribution of users among cells. This model is suitable for the future of Pico-cellular systems. The main assumptions of the model are: • A finite population of users moving in a finite set of cells • Users are indistinguishable from each other and pass from a cell to another following a probability transition patters with the same transmission rate • A parameter called µP, or the cell transition rate. The model assumes a FCA assignment for the channel frequencies. According to the results shown in [Camar98], the use of uniform channel allocation scheme is worse than the use of a non uniform one. In fact, minimum-blocking probability is obtained with a number of channels allocated to each cell approximately proportional to the number of users in the cell. Network Modeling Hexagonal cells arranged in (2R –1) rows, as shown in Figure 1 can represent an ideal network. As shown, there are R rows of K cells and (R-1) row of (K+1) cells. The total number of cells is M=RK + (R-1)(K+1). We assume N users circulating in the network. It is supposed that the occupation time of a user is defined by an exponential distribution with mean 1/µP i.e. the pdf of this random variable (called TP) is: f T p (t ) = µ P e − µ Pt 13
  14. 14. K-1 K 1 2 K+K+1 K+1 K+2 M-K-1 M- 2K M-K M-K+1 M-1 M Figure 1. Cellular Network As far as mobility is concerned, each cell is modeled by an infinite server to consider its occupation time. They also have assumed a probability of transition from one cell to another, indicated by Pij Now it is assumed a λI, for each cell, which is the effective arrival rate of users to the cell i. Where, λi = ∑ j λ j pij , where I=1,2,…. M, (1) M however this term is used in conjunction with nI is the number of users in the ith cell, and by n=(n1, n2, …. , nM), is the state vector for the system. The probability of a state n can be evaluated by: 1 M P ( n) = ∏ hi (ni ) ,(2) G 1 hi ( n i ) now the factor can be calculated by: ni 1 λ  hi ( ni ) =  i  ni !  µ P  (3)   where the arrival rate is given by (1), now the normalization constant G from (2) is calculated in the paper as: G=g(N,M), where g(N,M) is a recursive function defined by: g(n,m)=1, n=0; m=1…M 14
  15. 15. g(n,m)=hm(n), m=1; n=1…N n g (n, m) = ∑ hm (k ) g (n − k , m − 1) , n=1…N, m=2…M, k =0 the marginal state probability of the Mth cell is given by: 1 P ( nM = k ) = hM (k ) g ( N − k , M − 1) (4) G while the average number of users is given by: N E[nm ] = ∑ kP(nM = k ) = k =1 1 N = ∑ k ⋅ hM (k ) g ( N − k , M − 1) (5) G k =1 Using little’s formula, the true arrival rate can be easily calculated as: E ( nM ) λM ( N ) = = E (nM ) µ P (6) E (T p ) it can be also shown that, the Utilization of the queue M, that is cell M, are given respectively by: g ( N , M − 1) U M (N ) = 1− (7) G g ( N − 1, M ) X M (N ) = 1− (8) G In this case Xm which is the throughput is expected to be: λ M ( N ) = X M ( N ) (9) Cell modeling In addition to the Throughput and utilization equation mentioned in the previous section, [Camar98] points out the need to model de cells in the network and specific processes such as call blocking and hand-off blocking. For example, when considering the service offered to the users, the possibility to make a call, the cell can be represented by a finite population (n) in a M/M/m/m/n queue. This is a loss system where the maximum number of contemporary calls in progress is given by the number of channels m assigned to the cell. As a resulting equation, the steady state probabilitie is given by: 15
  16. 16. n γ k  ( ) k  µ Pk =   c , where k=0,1,….,m (10) m n γ ∑i=0  i ( µ )   i   c And the probability that a user in a call attempt does not find a free channel is given by the probability that all cell channels have been allocated to another users in the cell, and therefore:  n − 1 γ m  m ( µ )   PL = m   c (11)  n − 1 γ i ∑  i ( µ )  i =0    c in both equations (10) and (11), γ/µc represents the required load per user in erlangs, where γ is the average number of call attempts in the time unit per user and 1/µc represents the average call duration. In terms of call blocking, a state vector n=(n1, n2, …. , nM) is assumed. Then, the probability of the jth cell (which contains nj users) a new call attempt is blocked Pbj(nj) can be obtained from PL on equation 11. Assuming only mobile-to-land and land-to-mobile calls and a perfect wired network, the blocking probability of the entire cellular network is evaluated by a weighted mean of cells blocking probabilities, where: M nj PB (n) = ∑ Pb j (n j ) (12) j =1 N Which if applied to the average equation for the whole system, it is obtained: M N nj PB = ∑ ∑ Pb j (n j ) P(n j ) (13) j =1 n j = k j +1 N Where kj and P(nj) represent respectively the number of channels and the probability to have nj users in the jth cell. The index starts for nj ≤ kj because less users than channels the probability of blocking is zero. Now, it is also mention the way to model the hand-off blocking probability, which the probability that a user with a call in progress; passing from one cell to another one, does not find a free channel in the destination cell and thus the call has to be terminated. And by knowing the blocking probability it is easier to say that: 16
  17. 17. N −1 Pbhj = ∑ Pb (n n j = k j +1 j j ) P(n j ) (14) in addition to taking into account Pb and P(n), the equation must take into consideration the probability of transition, and the instant of transition it must consider N-1 users instead of N. The network hand-off blocking probability PBH is obtained by the weighed sum of cell hand-off blocking probabilities where the weights are given by the fraction of the arrival rate λaj(N) of users with a call in progress. M λ aj ( N ) PBH = ∑ Pbhj (15) ∑i=1 λai ( N ) M j =1 and the rate λaj(N) is given by: M λ aj ( N ) = ∑ X ai ( N ) pij (16) i =1 The results coming out of the model, represent an analytical solution. According to the paper the results provided were compared with a simulation executed in SMPL language, however no details and comparisons are explained, however for simulation purposes several parameters where used such as: B H H H +B PB = PBH = PFT = PUC = T T −H T −B T Where B represents the blocked calls, T the new tried calls, TH the tried with Hand-off, H the unsuccessful hand-offs. And FT stands for forced termination and UC for unsuccessful completion. There are several assumptions from this model, first the matrix for transition probabilities between cells, which can lead to have a non-homogeneous model in the network, but it requires son previous studies of the cells in the model. 17
  18. 18. REFERENCES [Camar98] P. Camarda, G. Shiraldi, et.al. “ Mobility and Performance Modeling in Cellular Communication Networks”, Mobile Computing and Communication Review, Vol.1 No. 4, 1998, 25-32. [Jue98] J. Jue, D. Ghosal “Design and Analysis of Replicated Server Architecture for Supporting IP-Host Mobility”, Mobile Computing and Communication Review, Vol 2, No. 3, 1998, 16-23, [Li98] Y. Li and V. Leung. “Supporting Personal Mobility for Nomadic Computing over the Internet”, Mobile Computing and Communication Review, Vol. 1, Number 1, 1998, 22-31. [Iera98] A. Iera, A. Fazio, et.al. “Hand-off management algorithms for urban and sub-urban environments under realistic vehicle mobility conditions”, IEEE International Conference on Communications v 3 1998. IEEE, Piscataway, NJ, USA,98CH36220. p 1375-1379 [Dell98] M. Dell’Abate, M. DeMarco and V. Trecordi “Performance evaluation of mobile IP protocols in a wireless environment” IEEE International Conference on Communications v 3 1998. IEEE, Piscataway, NJ, USA,98CH36220. p 1810-1816 [Mysore98] J. Mysore, B. Vaduvur. “Performance of transport protocols over a multicasting-based architecture for Internet host mobility” IEEE International Conference on Communications v 3 1998. IEEE, Piscataway, NJ, USA,98CH36220. p 1817-1823 18

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